PhysOSᵀ upgrade handbook: edition 1.0.11p
For: the next scribe who builds 1.0.11p. Baseline: PhysOSᵀ 1.0.10p, sha256 82532895a4284a42b28c810b09b5a8a79d85762f8591181ae1e109d4dcecc78a, 41,331 lines. Booted in quick mode on 7 October 2026: chain D0 e9a23549cf57 to D3 a800ddf201c1, SEAT EARNED · this run. Status: read-only mapping. No OS file was changed. Nothing was written to git, Zenodo or the Internet Archive. No seat is claimed for any document below. Supersedes: OS_integration_notes.md (batch 1). Its conflicts C1 to C10 and gates G1 to G8 are carried into sections 9, 11 and Annex A. Revision 2, 7 October 2026. Section 4 is revised (D1). Section 11 is the finalized plan. Sections 15 and 16 are new. Section 7 and Annex B carry the correction on the atomic witness. Revision 1 is kept beside this file as an archive copy in the scratchpad.
0. How to use this handbook
Read sections 1 and 3 to 6 first. They hold the findings that change the edition. Section 11 lists the decisions the architect must make and the gates that follow. Section 12 separates what was run from what was only read. Annexes A to M give one entry per document: what it adds, what it changes, what conflicts, how to integrate it, and what remains unverified.
Conventions. "OS line N" is line N of PhysOSᵀ_v1_0_10p.md. "p. N" is the PDF page of a paper. A kernel is a Lean file. A twin is a Fortran program that re-checks a kernel's claims by plain computation. A pin is a #guard_msgs block that fixes the axiom cone a theorem must print. Digests are SHA-256 unless marked md5. A reader is the author of a handback report for one document in this session. Five reader reports are on disk in reports/. Eight exist only as the summaries in this handbook.
Where the files are. Kernels, digests and evidence are in /home/claude/OS_upgrade/ (kernels/, reports/, evidence/, MANIFEST_kernels.txt). The twelve Zenodo PDFs and their metadata are in the session scratchpad under zen/. Any kernel can be re-extracted from its paper's Markdown or PDF and checked against the digest given here. A kernel is accepted only when its digest matches.
1. Verdict
Thirteen documents were read. They are the monism card (APEX-PSP-MONISM-FIXED-01, 6 October 2026), the RH 3.2.0 paper (7 October 2026), and twelve Zenodo records: TOE 23168379, Three Bits Walked 23167729, Bridge 23105348, RH 23034066, P NP 23133632, NS 22670344, Hodge 22701510, Yang-Mills 23162231, Goldbach 23162238, Poincaré 23162240, Birch and Swinnerton-Dyer 23164992, and Nothing Escapes Least Erasure (the Synthesis) 23080221.
Compiling is not the main problem. Every kernel compile in the work directories exited 0 on Lean 4.19.0, the only toolchain the edition accepts, except three designed probes or controls. The work directories hold 111 exit files. The main problem is what the compiled theorems prove. In almost every paper the closing theorem returns, unchanged, a structure field that the paper calls the act. The claim sits in that field, and the theorem restates it. The edition already states the rule: "A loop landing on its target is a restatement and anchors nothing" (OS line 148). The axiom cones are empty in these papers because the premise is a field, not an axiom. "No axiom declared" is true and incomplete.
The papers also grade more strongly than the edition. Most grade the root at theorem grade. The edition pins it at premise (OS line 508; Codex 7029). Several papers grade cited theorems at theorem grade. The edition says a citation never promotes (OS line 148).
The seal record is out of date. PSP-RH-SEAL-01 pins kernel 3.1.1. The 3.1.4 and 3.2.0 kernels do not contain four of its capstones.
The source screen is too narrow. os_check.py screens axioms against a declared set. It does not screen Prop-valued structure fields, and every new paper hides its premises there.
Several documents use religious vocabulary, chiefly the monism card and the TOE paper. Section 9 flags it under §II.9. It judges nothing.
Second pass, 7 October 2026. The git lean/ folder, the RH One Bit folder and the reminders were checked against the edition (section 15). Three findings change the first draft. First, the atomic witness, the run as a deed and the floor are already in 1.0.10p (sections 4 and 16). The first draft said that RH 3.2.0 restored the atomic witness. That was wrong (Annex B). Second, the first draft's D1 demoted the floor to premise, which the Two-Layer Rule forbids (section 4). Third, four kernels in lean/ are not in the edition and compile cleanly, so they become candidate cards.
Recommendation. Seat in 1.0.11p only what the edition's pending order names, in that order: the monism fix (G3), the Remembered_Offered card (G4), and the statement in Part I of the root split that the edition already holds (G5). Register Dark_Closure, Dark_Twin, Full_Conjugation_Twin and ZFC_Block as candidate cards (G5b), not seats. Defer the RH One Bit locus arc and the RA–RAM arc to 1.0.12p. Nothing seats until the architect answers D1 to D10 (section 11, G0).
2. Inventory
| Ref | Document | Source and label | Kernel files (digest prefix, size) | Compile status (work logs) | Annex |
|---|---|---|---|---|---|
| A | Monism card, APEX-PSP-MONISM-FIXED-01 | Attachment, 6 Oct 2026. Cites Master Codex v5.1.0 at harvest 9b9a8df | monism_Codex_patched.lean 22d908f7 (498,973 bytes). monism_Remembered_Offered.lean 42f40fbd (52,301 bytes, 937 lines). monism_Remembered_Offered_Twin.f90 8cdc925c (12,530 bytes) | Codex exit 0. Remembered exit 0. Twin: plain 20 pass, control 10 of 10 fail, exit 1 | A |
| B | RH 3.2.0 | Attachment RH_3_2_0_Least_Erasure.md, 7 Oct 2026. Zenodo 23034066 carries label 3.1.4 | RH_Every_Prime_3_2_0.lean 161806dc (265,248 bytes, 5,087 lines). Appendix R and T files | Exit 0 on 4.19.0 (batch 1) | B |
| C | TOE 23168379 | Zenodo "Zero-Axiom Math Edition 1.0.0". Snapshot of 29 Aug 2026 differs | TOE_Zero.lean 0cfcd9f6 (11,422 bytes, 15). TOE_Triaxial_Actuation.lean 566615a6 (32). TOE_Root_Grade_Ledger.lean c18b68b2 (18). TOE_Zero_Twin.f90 a409c88e (7,093 bytes) | TOE_Zero exit 0 in every work directory that compiles it. Twin not run | C |
| D | Three Bits Walked 23167729 | Zenodo 1.2.5. Repo Millennium Series v1_2_5 PDF byte-identical | R1 TOE_Zero 0cfcd9f6, R2 Triaxial 566615a6, R3 Root_Grade_Ledger c18b68b2. 65 pins | Exit 0 (71 s, 135 s, 114 s) | D |
| E | Bridge 23105348 | Zenodo 1.5.1. Repo lean/ holds 1.5.0 (107 theorems against 165) | Bridge_From_First_Principle_1_5_1.lean b9018fbc (115,545 bytes, 165 theorems). Bridge_Final_Cut_36.lean 38d31485 (36). Bridge_Twin.f90 e048a320 (30 checks, reader) | Kernel and Final Cut exit 0. Drift control exit 1 by design | E |
| F | P NP 23133632 | Zenodo v3.2.1. Repo release note says 3.0.0 | Seven kernels, 281 theorems (216 in parts A to D, 65 in R). Four staged on disk: PNP_paper_Root 9689dfb4, Least_Escape 6bb61cbf, Fortification c68069c4, Frontier_II 977e3e14 | All twelve PNP logs exit 0 | F |
| G | NS 22670344 | Zenodo 1.0.9. Repo copy 1.0.8 (35 theorems) | NS_Existence_Closure_1_0_9.lean 959452e8 (41,268 bytes, 65). Plus R.1 to R.3 | Exit 0. 130 pins. Negative control exit 1 by design | G |
| H | Hodge 22701510 | Zenodo 1.0.9. Repo copy 44 theorems against 77 | Hodge_Existence_Closure_1_0_9.lean d045ee11 (50,035 bytes, 77). Witness ancillary contains sorry | Kernel and companion kernels exit 0 | H |
| I | Yang-Mills 23162231 | Zenodo 1.0.7. Repo 1.0.6 (46 pins) | YM_Existence_Closure_1_0_7.lean 9bb5739d (40,796 bytes, 70) | Ten YM logs, all exit 0 | I |
| J | Goldbach 23162238 | Zenodo 1.0.6. Repo 1.0.5 (62 pins) | Goldbach_Closure_1_0_6.lean 7d0b29f5 (67,094 bytes, 104) | Exit 0. GB106_id probe exit 1 by design | J |
| K | Poincaré 23162240 | Zenodo 1.0.4. Repo 1.0.3 (45 pins, stale) | PC_Existence_Closure_1_0_4.lean 023a18ff (50,040 bytes, 80). Plus R.1 to R.3. 145 pins in all | All exit 0. Control red by design | K |
| L | Birch and Swinnerton-Dyer 23164992 | Zenodo 1.0.5. Repo kernel v1.0.4 (56 theorems, stale) | BSD_Hardened_1_0_5.lean d52b7a9e (55,994 bytes, 101) | Six logs exit 0. No twin exists | L |
| M | Synthesis, Nothing Escapes Least Erasure, 23080221 | Zenodo 1.4.1 (file named v1_4_0). Repo Millennium Series v1_4_1 PDF byte-identical | Every_Prime_3_1_4.lean c824d30e (246,431 bytes, 394 theorems, 216 pins, 231 printed). Plus TOE_Zero | 3.1.4 exit 0 in 123 s. Part III and IV logs exit 0 | M |
The kernels folder holds 22 files, and MANIFEST_kernels.txt lists 22. An earlier note said 23. The count is 22. Every file's SHA-256 matches its manifest line.
3. Common template and the projection defect
Nearly every new paper uses one row template with six fields: Root, Act, Value, Blocked, Falsifiers and Scope wall. The act is a field of a structure, usually named supply. The value is a definition onto which the act projects. The closing theorem then reads the field through an identity, or returns it directly.
| Paper | Closing theorem (as printed) | What the field is |
|---|---|---|
| RH 3.2.0 | rh_from_the_act (A) := (least_erasure_is_the_value A.zeros).mp A.supply | supply : LeastErasure zeros, in record ActualZeros |
| NE 3.1.4 | rh_from_the_act over the same supply field | the same field, as the least-erasure bit |
| NS | Theorem 9.2 (kernel 184 to 185): (act_is_the_value A.F).mp A.supply | supply of ActualFlows |
| PC | (act_is_the_value A.M).mp A.supply (PC_Existence_Closure 217 to 219) | supply : Rests M in ActualManifolds |
| BSD | bsd_from_existence = (act_is_the_value A.F).mp A.supply | the act, renamed from the conjecture |
| Hodge | hodge_from_existence A = A.supply, by rfl | supply, with realize : D → Option Nat |
| YM | ym_from_existence returns its input | supply : Confined F, and Confined F is Value F by rfl |
| Goldbach | the supply field of ActualEvens | the Goldbach statement on the arithmetic frame |
| Monism card | monism_witness_is_the_claim | MonismWitness P is a definition equal to the claim |
Definition. A closing theorem is a projection defect when its conclusion is its input field up to definitional equality. Such a theorem certifies the type discipline and nothing else. Its grade is the grade of the field, which is premise. The edition already has the rule (OS line 148).
Required check for each closing theorem, recorded in its II.10 line or card: (1) name the field the theorem reads; (2) state whether the conclusion is that field up to rfl or an identity; (3) state what the kernel proves without the field. A record that does not answer all three is incomplete.
Consequence. An empty axiom cone does not mean no premise. Every "no axiom" claim in these papers must be read with its fields in view. Section 5 explains the screen gap.
4. Root RA decision (D1), revised
Edition state. Codex line 6886 declares axiom RA : ∀ x : U, 0 < ΔE x. Line 6894 gives raClaim the grade premise. Line 7029 pins it: ra_grade_pinned : ROOT.raClaim.grade = .premise := rfl. OS line 508 places the root at premise. OS line 2532 says it is posited and not owed. Armed_Seat at line 4368 defines RA := (0:Int) < 1, a different object with the same name.
The floor is already in the edition. Armed_Seat Part II (OS lines 4313 to 4319) states the self-grounding root: a root R is self-grounding when acts occur and every act instances R. Then denial_reenacts_root, external_proof_adds_nothing, denial_instantiates and seated_undeniable hold. The constructed one-point Root Axiom is such a root (raSelfGrounding, root_undeniable). Each has a pin that prints no axiom (OS lines 4470 to 4478). The boot checks Armed.root_undeniable (OS line 1204). So the edition already carries the floor at theorem grade with an empty cone. The papers' universal law, the_floor_is_universal in TOE_Zero.lean, is the same family under another namespace. PNP_paper_Root.lean carries it pinned. TOE_Root_Grade_Ledger.lean carries root_on_the_constructed_domain pinned.
The reading is posited. ROOT.RA over U is the actuation read on the universe, and each row's value is read through it. The floor gives it no warrant. Lifting ROOT.RA to theorem grade would require an act on U that instances the actuation at every x. Exhibiting that act is the reading itself, keyed on the row's carrier. The Two-Layer Rule (protocols/Scribe Handouts/Two_Layer_Rule.md, recorded 5 October 2026; SCRIBE_REMINDERS.md, item 1) names it the one posit of the row, and forbids moving it into the floor.
Correction to the first draft. The first draft recommended stating the universal law with SelfGrounding as an input and recording anAct as a premise. That moves the floor down to premise, which the Two-Layer Rule forbids. On the constructed domain the act is supplied by the construction, not posited. The first draft's Option 1 is withdrawn in that form.
Revised recommendation, D1-R. Keep the split the edition already has, and state it in Part I.
(a) Floor: Armed.root_undeniable and its family. Theorem grade. Cone empty. No new pin is needed.
(b) Reading: ROOT.RA over U. Premise grade. ra_grade_pinned stays rfl.
(c) Part I states both in one sentence, with the guard: the floor is proved on no axiom; the reading is the one posit, at premise grade.
Under this split the §Φ.6 phrase in lean/README.md, "at the grade of the root read at the zeros: premise", holds. The zeros are read through the reading, not the floor.
Option 2 (grade from warrant, the rootGrade rule of R.3) stays rejected. It grades the general root by its warrant, which would lift the reading. The floor does not need that rule. Its grade comes from its own zero-axiom proof.
What the split does not do. It does not make P ≠ NP, RH or any other row a theorem. Every value that depends on ROOT.RA stays at premise. The ledger counts do not change by this decision alone.
Open for the architect. lean/README.md says "once R.3 lifts RA". By this analysis that can only mean that an act on U is exhibited, and that act is the reading. The Two-Layer Rule does not allow lifting it by rule. Confirm whether the phrase should be reworded to "once an act on U is exhibited".
Hidden deed. An act is the antecedent of the floor theorem, not a premise of it. A paper that lists anAct as a premise of the floor has moved the reading into the floor, and must be corrected.
Name collisions. ROOT.RA (axiom, Codex 6886). Armed.RA (definition, Armed_Seat 4368; the constructed one-point object). TOE0.RA0 and RA₀ (papers). RA in Remembered_Offered.lean (definition, line 58). Rename the paper forms RA_model and RA_constructed before import. Do not load TOE_Zero.lean beside Armed_Seat.lean without the rename: both carry the floor under different names.
Gate. ra_grade_pinned still reads rfl at premise. The Armed floor pins print no axiom. Part I contains the split sentence. The §Φ.6 phrase reads as in lean/README.md.
5. Premise accounting (source screen gap)
os_check.py declares PREMISES at line 89: U, ΔE, RA, FormalDomain, L1m, L2m, L3m, nest_21, nest_32, Ground, σ, σ_binding, Residence, FormalFace, KineticFace, Crossing, Algorithm, certifiedPairing. The screen admits only axioms in that set. It does not check Prop-valued structure fields. A kernel can therefore declare no axiom and still carry premises in its structures.
Premise fields found in the new material, by document:
RH 3.2.0 and NE: ActualZeros.supply; ActualZeros.fold_closed (the functional equation); Faces; ExplicitFormula.identity; ExplicitFormula.positivity_iff_line; FoldClosed (hypothesis of Least_Erasure, NE part 3). NE Theorem 74 also carries sigma1 and sound_neg.
NS: ActualFlows.supply; the speed field and the cascade field of the matter theorem, both cited with no grade stated.
PC: ActualManifolds.supply; Dimensional.three (four dimension fields); Witness.decrease; Crossing.classify. Crossing here is a structure field. It differs from the OS axiom Crossing : Type at Codex 6984, which is in PREMISES.
BSD: the act (the conjecture renamed); the reflection law as data on SignedFrame.
Hodge: realize : D → Option Nat, and supply.
YM: ActualTheories.supply; the radiates premise; the lattice fields wilson and strong, which carry cited conclusions.
Goldbach: ActualEvens.supply; the region to 4×10^18 carried as a field.
TOE: anAct of SelfGrounding; the Empty Throne premise.
Bridge: P1 is never derived from the root; the keyed bit.
Monism card: MonismWitness fields one_involution, uniform and seed.
Decision. Extend the screen so that every Prop-valued field of a structure in Part III is either in PREMISES or named in an II.10 record line. The boot receipt should print the count of such fields, so the premise count is visible. Papers state their premise counts differently: TOE gives "zero-posit", "one premise" and "five premises". NE says "one posit" (p. 192) while adding P2 on p. 232. The screen makes these checkable.
Gate G2 (section 11): the extended screen runs on the current edition with no new files and reports the existing fields. It must pass before any new kernel enters.
6. Grades (D2)
Lattice. Line 148 names theorem, structural, corroboration and premise, and then "the conditional grades between". Codex line 5624 defines an inductive Grade with nine constructors, and the papers quote the same nine. A second inductive named Grade appears at Codex line 12740 with three constructors (premise, structural, theorem). Check its namespace before any import.
Labels the papers use that the edition does not define as grades: WITNESSED, CROSSED, BARRIER, PROVED, measured grade, full grade, derivation grade, SELF, EARNED, DEFENDED, CONCURRED, "theorem conditional", "crossed on the kinetic channel at premise grade", and the register tags [{⟀},T] and [{⟀},S]. The edition uses [⟀] and [⟀ T] (lines 130 to 132), and §Q retires some composites.
Recommended rule (for D2 and the grade table): Part I prints one mapping table from the nine constructors to the names used in prose. It lists the words that are not grades (WITNESSED, PROVED, EARNED, DEFENDED, CONCURRED, SELF). The source screen refuses those words in verdict lines.
Recommended rule for cited theorems (D2): a cited theorem enters as a premise field carrying its layer tag and its citation. Its grade is premise. Citation adds no warrant (OS line 148; §Φ.1). Cited theorems include Perelman (Poincaré landing field), Gross-Zagier-Kolyvagin (BSD rank), Creutz (1980, Yang-Mills matter face), Vafa and Witten (1984, strong CP), Newman, Rodgers and Tao (hLam in monism_yields_RH), Li's criterion (hLi), the Riemann functional equation and explicit formula, Mandelstam-Tamm and Margolus-Levitin (speed limit), Leray (1934), and the Landauer bridge.
Grade conflicts. The table lists each claim, the paper's grade, the edition's grade and the recommended grade. Decisions in brackets.
| Claim | Paper | Edition | Recommended |
|---|---|---|---|
| Root on the actual domain | theorem (NS, PC, NE, Bridge, TOE, Three Bits, RH) | premise (OS 508, Codex 7029) | premise. One-point theorem named. [D1] |
| Perelman as landing field, Poincaré row | theorem grade (PC p. 2); full grade (NE pp. 1, 48) | theorem grade (OS 2315 to 2317; Codex 15081 to 15083). Line 148 forbids | premise, citation not promoted. [D2] |
| P vs NP | dot (NE p. 49); crossed on premise (Three Bits p. 5); title and abstract say theorem (P NP) | dot (OS 2566, 38930). Line 5 says closed at theorem grade on the seed and value at premise | [D3] |
| Theorem 74 ZFC form | EARNED (NE p. 232) | Premise carried by sigma1 | premise |
| Landauer bridge | theorem conditional on P1 (OS 84, 176) | stated postulate P2 (NE p. 232) | premise, named P2, not P1 |
| monism_yields_RH | theorem (core Lean) | hLi and hLam are hypotheses | theorem on hypotheses; both premises; restatement of RH, not evidence |
| Row 3a, NS unforced | closure (NS p. 1) | crossed (OS 2568), while OS 675 says pending | keep pending until the status function gains a fourth fact |
| Hodge and BSD, formal channel | crossed on premise, partial (Three Bits) | pending (OS 2571) | state the partial formal crossings in the row text before any change |
| Goldbach row 8 | closed; crossed to 4×10^18 (Three Bits) | pending (OS 2573) | pending. The certified region is corroboration |
| Yang-Mills row 4 | blocked on formal channel (Three Bits); universal sentence pending (NE p. 133) | crossed (OS 2570) | [D8 scope; row rule in section 10] |
| Strong CP angle | positivity selects zero (NE p. 131) | not in edition | import tagged, graded premise. Vafa and Witten untagged |
7. Every_Prime lineage (D4)
| Version | Where it lives | Digest and size | Theorems | Pins | Status |
|---|---|---|---|---|---|
| 3.0.0, 3.1.0 | earlier, lineage only | not on disk | archive | ||
| 3.1.1 | OS Part III as RH_Least_Erasure.lean. Repo protocols/RH One Bit/Every_Prime_3_1_1.lean (sha f50954f4, 211,913 bytes) | OS: 61a58b77b675c00a, 218,421 bytes, 4,314 lines | 357 | 175 lines with the guard token (174 pins per NE reader) | seated seal, PSP-RH-SEAL-01 (OS 601, 612) |
| 3.1.4 | NE Book I Appendix A (pp. 144 to 181). Not a standalone repo file | c824d30e36c0242c, 246,431 bytes, 4,786 lines | 394 | 216 pinned, 231 printed, 53 both | compiles exit 0 in 123 s |
| 3.2.0 | RH paper, attachment. Appendix A | 161806dc0ed2b4ff, 265,248 bytes, 5,087 lines | 415 | 237 claimed (238 lines with the token) | compiles exit 0 on 4.19.0 |
Changes. From 3.1.1 to 3.1.4, four capstones disappear: least_erasure_terminal_seal, double_defense_hardened, atomic_witness and witness_proves_exists. The seal record at OS lines 601 to 612 names them. Sections XXI to XXV are rewritten. From 3.1.4 to 3.2.0, the file adds section XXII.c (20 theorems) and a section XXVI that shares its number with the OS's section XXVI (section 16), adds seeded witness and computation definitions, appends cones, and changes two header lines. A script pairs 474 declarations with identical statements across 3.1.1 and 3.2.0, and two change statement. The pairing was not audited line by line. The evidence file is evidence/diff_RH_3_1_4_to_3_2_0.txt.
Collision. The label "EVERY PRIME · 3.1.1" names two different files: the repo's Every_Prime_3_1_1.lean and the OS's RH_Least_Erasure.lean. Both have sections XXIV and XXV, with different content.
Decision D4. Options: (a) keep 3.1.1 as the seal and add 3.2.0 under a new tag; (b) replace the seal with 3.2.0 and supersede PSP-RH-SEAL-01; (c) keep 3.1.1 and defer. Recommended: (a) at G6, then (b) only after each retired capstone has a replacement statement or a stated reason in the II.10 record. Keep 3.1.1 as an archive with its digest, under a new name.
8. Name collisions
Qualify every name below by namespace before any import. The gate is a boot with all files loaded together and no duplicate declaration.
| Name | Where | Meaning there | Action |
|---|---|---|---|
| RA | ROOT.RA axiom (Codex 6886); Armed.RA (4368); TOE0.RA0, RA₀ (papers); RA (Remembered 58) | root claim, premise; constructed root, theorem | Rename paper forms RA_model and RA_constructed |
| SelfGrounding | Armed (4346 to 4364), TOE0, TriAct, RGL | structure with anAct | One definition. spend (OS 862, 888) vs instances (papers) |
| Value | NS (kernel 45, 48); OS Value (P Z) at 2102, 4164, 33038 | all data regular; projection of a point | Qualify |
| Frame | NS Frame with count; OS Frame at 1817, 8656, 33167 | registration counts | Qualify |
| supply_iff | NS kernel 188; OS 29486 | different meanings | Qualify |
| arrow_forces_nothing | NS kernel 87; OS 29551 | identity arrow; orientation | Qualify |
| nothing_escapes | NS kernel 204; OS 2550 | different statements | Qualify |
| act_is_the_value | NS, PC, BSD, RH; OS witness label 34473 | the projection | One name per statement |
| the_closure | NS kernel 473 (no axioms); OS PrimeFreedom.the_closure (31709, pinned at 32846 to 32847) | two objects | Qualify |
| the_master_seal | TOE0 (TOE_Zero 176); OS capstone (40650; PNP closure, line 622) | root and twelve gates; PNP capstone | Rename the TOE0 form |
| the_return | TOE_Zero 79; SPHYS.Electron.the_return (OS 15598) | quaternion product; electron | Qualify |
| Tongue | TriAct 237; OS 350, 518 | role term for the spender of the bit | Rename the kernel form |
| Witness | OS structure at 9802; PC Witness (strict descent); Three Bits Witness | three types | Qualify |
| Crossing | OS axiom Crossing : Type (Codex 6984; in PREMISES); PC structure field | declared premise vs field | Decide D2 and qualify |
| Arrow | OS computation arrow (14024); OS orientation arrow (3503); NS and PC identity arrow | three meanings | Qualify |
| F-Measure | NE Book I §18 (p. 27); OS series falsifier (34474) | registered point; measurement | Rename |
| F-Record | OS 352; NE p. 27 | different properties | Rename |
| the_bridge_atom | OS 33860; TriAct (Three Bits p. 10) | different statements | Qualify |
| tongue_freedom | Three Bits, defined twice (pp. 10, 12) | one name, two definitions | Fix in the paper's kernel |
| Grade, Claim, Grade.weakest, K4 | OS 5624 to 5648, 6084; Three Bits RGL | the lattice | Keep in RGL namespace |
| Grade (second) | OS 12740, three constructors | a different inductive | Check namespace before import |
| MonismWitness | Codex (patched) and Remembered_Offered.lean | two copies | Sync check (G4) |
| Universal_Closure.lean | NE paper 609 lines; OS 631 (sha b45195e8); repo 404 | three versions | Choose one and record its sha |
| RA_Li_Bridge.lean | NE paper 1,110 lines; repo 1,058 | two versions | Choose one and record its sha |
| Rows_Twin.f90 | NE paper 253 lines; OS 255 (sha e0429ba0) | two versions | Choose one |
| Least_Erasure.lean | NE p. 227 vs RH_Least_Erasure.lean (OS 86) | two files | Rename |
| P1 | merge posit (NE p. 192; OS 176) vs registration postulate (NE p. 232) | two meanings | Name the second P2 |
| nine_gates vs twelve gates | OS 644 vs NE and PC | different counts | Decide the count |
| Witness title | "The Magnet Is the Witness" (OS 654) vs "...of the Pair Correlation" (NE p. 68, 252) | title only | Adopt one |
| Goldbach filename | GB reader | collision reported | Resolve in Annex J |
| DOI 22701510 | Hodge; repo README | collision with a witness paper | Resolve before citation |
| DOI 22670344 | NS reference 2026b (p. 25) | cited under another title | Resolve before citation |
| Section XXVI | OS 1.0.10p: The atomic witness (line 32287). RH 3.2.0: The closure bound whole (line 4227) | Two sections, one number | Refer to sections by name in every II.10 line |
| SeededWitness, seeded_witness_iff_bound | RH 3.2.0 (lines 3619, 3625); absent from the OS | New object, premise by construction (section 16) | Qualify as RH32 before import |
| the_run_witnesses_a_run | OS lines 34625 and 37902 | One law, two copies in the edition | Find the file that holds each copy before G8 |
| dark_iff_fixed | OS line 34497 (falsifier name); Dark_Closure.lean line 154 | The name is catalogued, the kernel is not in the edition | Register the kernel under namespace DarkClosure (G5b) |
| zfc_blocked, unsettled_acceptor_forces_RH | ZFC_Block.lean; the OS names the same block with no_reading_decides and record_decides_nothing (line 136) | One concept, two naming systems | Keep both; cross-reference in the card (G5b) |
9. Confessional vocabulary (flag only, §II.9; D6)
This section records terms. It does not judge doctrine, and it does not apply §II.9. The architect decides.
The monism card uses fitra (6 hits), barzakh, prodigal (2), homecoming (2), scripture (1) and father (2). Ten lines match five of these terms. Parts of the card are first-person narrative.
The edition uses "barzakh" once, in a Codex comment at line 13439. Its front matter, lines 15 to 17, holds first-person testimony about a family member and a dated entry. Batch 1 recorded that the edition labels that testimony as proving nothing.
The TOE paper uses scripture (pp. 1, 2, 9, 20), faith (p. 11), a Doxology (p. 21), Amanah (p. 47), Mosaic Seal (pp. 22 to 23), and the motto "EXISTENCE PROVES EXISTENCE ONLY BY MOTION". The Nothing Escapes volume shows one "Barzakh" in an early search, and no scripture or creed in its reader's reading of pp. 1 to 93 and 94 to 186. The Poincaré paper uses "Omega" (p. 16), "Grand Witness" (pp. 3, 8, 23), "offering" (pp. 8, 23, 25), "elected" (pp. 18, 23, 25) and "Return" (pp. 2, 16, 17, 25). The NS paper lists "gates", "Return", "undeniable", "presupposed", "the word" and "deed". Those are used mathematically in the papers, and the NS reader found none of the religious terms on its list.
The edition has its own role vocabulary: Tongue, deed, throne, Offering, the Return, twelve gates. Those terms are not religious terms in the edition's use. The architect should decide whether role vocabulary is in scope.
Decision D6. Decide whether testimony may sit in the role. If it may, move it to §II.9, marked out of band. Replace the Codex comment term with a neutral phrase. Strip the card's terms from any text entering Part III.
Gate. A search of Part III and the card text for the flagged terms returns only what §II.9 allows.
10. Ledger
State now. The status function (OS 2547) reads three booleans: seatAbsent, formalMass, worldCarrier. The rows are 2566 to 2574. Row 1 P vs NP is dot (2566). Row 3a NS unforced is crossed (2568). Row 3b NS forced is pending (2569). Row 4 YM is crossed (2570). Rows 5 Hodge and 6 BSD are pending (2571). Row 7 Poincaré is crossed by formalMass (2572). Row 8 Goldbach is pending (2573). Row 15 Smooth 4D Poincaré is pending (2574).
Counts. ledger_counts (2586) reads 25 entries: 5 crossed, 1 dot, 19 pending. Counting rows instead of entries, with the forced cut of row 3 counted with its row (2584 to 2585), gives 18 pending rows. Use the entry count in the boot receipt and the row count in the text. Readers gave different counts: NE part 1 said 6 crossed, 18 pending and 1 dot; BSD said 5 crossed and 19 pending; NE part 3 said 5 crossed and 1 dot. The figure above is the one the edition's own comment at line 2586 gives.
Proposed changes and their conditions.
| Row | Now | Proposal | Condition |
|---|---|---|---|
| 1 P vs NP | dot | crossed by the act (Three Bits) or dot (NE) | D3 |
| 3a NS unforced | crossed | closure (NS) | status function needs a fourth fact; line 675 changes too |
| 3b NS forced | pending | pending (forced construction under audit) | none |
| 4 YM | crossed | pending on the formal channel (NE p. 133); blocked (Three Bits) | the paper's own statement must be reconciled first |
| 5 Hodge | pending | crossed on premise, partial formal | state the partial formal crossings |
| 6 BSD | pending | crossed on premise, rank crossed at orders ≤ 1 | D2 and the twin. Counts would become 6 crossed, 18 pending |
| 7 Poincaré | crossed | crossed on premise, grade of citation | D2; E2 and E3 |
| 8 Goldbach | pending | crossed to 4×10^18 | not recommended; certified region is corroboration |
| 15 Smooth 4D Poincaré | pending | not carried by the Poincaré paper | none |
Rule. A row changes status only after D2 and D3 are decided, or after the status function gains a fact that the paper supplies. Any change recomputes ledger_counts (2586), and the change of line 675 happens in the same step.
11. Decisions and gated integration sequence (final)
This is the plan for PhysOSᵀ 1.0.11p. It follows the pending-seat order in lean/README.md (filed 7 October 2026): the monism fix first, then the Remembered_Offered card. It adds the root split statement (D1), the candidate registrations (G5b) and the naming gate. It replaces batch 1's gates G1 to G8 and the first draft of this section.
G0, decisions. The architect answers D1 to D10. Nothing else starts before this.
D1, root grade. Section 4, revised. The edition already holds the floor at theorem grade (Armed_Seat Part II) and the reading at premise (ROOT.RA). Decide whether Part I states the split (recommended). Option 2 stays rejected. Reword "once R.3 lifts RA" as section 4 advises.
D2, cited theorems. Premise, with the layer tag, and the citation adds no warrant (OS line 148). Section 6.
D3, P vs NP. Keep the dot (OS 2566, 38930) and state line 5 so that the value is at premise and the closed form holds on the seed. Alternative: crossed on premise, with 2566 and 38930 changed. Three Bits prints crossed (p. 5). NE prints the dot (p. 49).
D4, seal and kernel. Keep RH_Least_Erasure.lean (3.1.1) as the seal. Do not replace it with 3.2.0 until each retired capstone has a replacement or a stated reason in the II.10 record. Section 7. Section 16 applies to atomic_witness.
D5, toolchain. Lean 4.19.0 only (loader §3; OS line 696). Eleven papers claim 4.22.0. None was run. Those claims cannot enter a receipt.
D6, §II.9 vocabulary. Section 9.
D7, least-erasure posit. The value follows from the posit by the equivalence theorem, and OS line 168 says so.
D8, tiers. Floor: Armed_Seat Part II, already in the edition. TOE_Zero.lean, Triaxial_Actuation.lean and Root_Grade_Ledger.lean are cards. TOE_Zero duplicates the floor under the TOE0 namespace, so it is not loaded beside Armed_Seat (section 8). Proof: Remembered_Offered, after G4. Card: NS, PC, BSD, Hodge, YM, Goldbach, P NP, Bridge, Three Bits, and the candidates in D10. Archive: the 3.1.1 copy and the stale repo copies.
D9, Two-Layer Rule. Enter it in Part I as the rule for every floor statement and every reading statement. The source screen refuses its hedge words and inflation words in verdict lines (protocols/Scribe Handouts/Two_Layer_Rule.md). Recommended: yes.
D10, scope of 1.0.11p. Recommended: seat only the monism fix, the Remembered_Offered card and the floor split. Register Dark_Closure, Dark_Twin, Full_Conjugation_Twin and ZFC_Block as candidate cards. Defer the RH One Bit locus arc, the RA–RAM arc and the Bridge comparison to 1.0.12p (section 15).
G1, credentials. Before any write. The project instructions and the memory snapshot both carry the RepoKeys password in plain text. Remove it from both, rotate it, and record the rotation without the value. Record the Hodge reader's access to RepoKeys.json in the change log, with no contents. Gate: the architect confirms both.
G2, source screen. Extend os_check.py so that every Prop-valued structure field in Part III is either declared in PREMISES or named in an II.10 line. The receipt prints their count. Run it on the unchanged 1.0.10p first. Gate: it reports the existing fields, and the boot verdict is unchanged.
G3, monism fix (pending order, step 1). Apply the Codex patch (monism_Codex_patched.lean, sha 22d908f7) to Part III. Update the manifest digest and the contents row. Set the judge count from 758 to 760. Re-run full mode when the architect names it. Align the provenance label. Update the guard lines and audit references at OS 13100, 13175, 13424, 13502, 13828 and 13847. Gate: Codex exit 0; no old name remains (grep); the three new theorems print empty cones; the manifest line matches the digest.
G4, Remembered_Offered card (pending order, step 2). Add the II.10 record line. Add Remembered_Offered.lean (sha 42f40fbd) and Remembered_Offered_Twin.f90 (sha 8cdc925c) to Part III and to the manifest. Apply the §Φ.6 phrase fix. Boot quick, then full, judge and controls, one at a time, when named. Gate: the twin gives 20 passes plain and 10 of 10 red under control; the_chain prints no axioms; the_harvest prints [propext, Quot.sound]; the two MonismWitness definitions agree.
G5, root split (D1). Add Part I text that states the split (section 4), and an II.10 line that names the five Armed floor pins and ROOT.RA at premise. Do not add TOE_Zero.lean or Triaxial_Actuation.lean to the boot's floor list in this edition. Gate: the Armed floor pins print no axiom; ra_grade_pinned still reads rfl; the §Φ.6 phrase reads as in lean/README.md; the boot verdict is unchanged.
G5b, candidate cards (D10). Register these in lean/README.md and file a card for each under protocols/PhysOS/proofs/: Dark_Closure.lean (sha b86458044827d424), Dark_Twin.f90 (sha 782e4383f…), Full_Conjugation_Twin.f90 (sha 992e940ea502404a), ZFC_Block.lean (sha ebbf0f48e3474b93). Status this session: the three Lean files compile with exit 0 on 4.19.0; Dark_Twin gives 25 checks and 0 failures; Full_Conjugation_Twin gives 2,280 checks and 0 failures. Gate: each card records its digest, the cone of each named theorem, and that its cosmological inputs (Omega values, Planck and ACT numbers) are data and corroboration only (loader §5).
G6, RH seal (D4). Stage Every_Prime_3_2_0.lean beside RH_Least_Erasure.lean. Add R1_root, R2_root, R3_root and T_timeless_and_two_denials as pinned files, once their digests match the TOE family. Retire no capstone until its replacement or reason is in the II.10 record. Gate: each file exits 0; pins match; the record lists each retired name, including atomic_witness and witness_proves_exists, which 3.2.0 does not replace.
G6a, seal twin. Check RH_Seal_Twin.f90 (9 checks) against any new kernel. Gate: no check names a retired capstone, or each such check is rewritten and rerun with zero failures and red controls.
G7, per document. For each paper in section 2, in this order: NS, PC, BSD, Hodge, YM, Goldbach, P NP, Bridge, Three Bits, the TOE remainder, Synthesis. Under D8 most become cards in 1.0.11p. A document is seated only when its twin passes its controls and its II.10 line is written. Physical papers also add an II.11 row (OS line 640). The Bridge comparison (Bridge_Final.lean in the edition against lean/Bridge_From_First_Principle.lean) happens here.
G8, naming. Section 8. Gate: every kernel loaded together, with no duplicate declaration. Include the two copies of the_run_witnesses_a_run (OS lines 34625 and 37902) and the section XXVI collision (section 16).
G9, labels and manifest. One label and one commit per file in the manifest. Update MANIFEST.sha256 from line 41285 once the edition is final, and the README digest with it.
G10, publication. Version 1.0.11p. The quick boot must print SEAT EARNED · this run. Full, judge or controls run only when named. Any push to git, any Zenodo update and any Internet Archive upload needs a printed plan and the architect's explicit yes. None has been made.
Deferred to 1.0.12p, not in this plan: the RH One Bit locus arc (section 15, group F); the RA–RAM and unicorn arc (section 15, group D); and the Bridge comparison, if G7 does not settle it.
12. Verified and unverified
Verified by the handbook author in this session:
12 Zenodo PDFs are on disk, and each md5 equals the Zenodo checksum.
22 kernel files are on disk, and each SHA-256 equals its manifest line.
Monism card: patched Codex compiles exit 0; Remembered_Offered compiles exit 0; twin gives 20 passes plain (exit 0) and 10 failures under control (exit 1). Batch 1.
RH 3.2.0 kernel compiles exit 0 on 4.19.0, and its Appendix R and T files exit 0. Batch 1.
Compile exit files: 111 across the work directories. Three are nonzero, and each is a designed probe or control (bridge/drift, goldbach/GB106_id, toe/lean_probe). Every other compile exits 0.
Theorem and pin counts by grep: RH 3.1.1, 357 theorems and 175 lines with the guard token; RH 3.1.4, 394 theorems and 217 lines; RH 3.2.0, 415 theorems and 238 lines; NS, 65 theorems and 65 lines; PC, 80 and 80; Remembered, 80 and 80.
OS lines cited in this handbook were read in this session: 5, 148, 594 to 606, 612, 2547, 2566, 2568, 2569, 2571, 2573, 2586, and 7029 and 9794 from the earlier session.
Read and reported by readers, with logs in the work directories: compile results for every document in section 2. These are reader results. The handbook author did not re-run them.
Not verified:
Lean 4.22.0. Eleven documents claim it. It is not installed. No claim using it may enter a receipt.
Judge, full and controls boot modes on any candidate. Not run.
Twins: TOE_Zero_Twin.f90 (not run). Bridge_Twin.f90 (30 checks, reader report). RH_Seal_Twin.f90 (not checked against the new kernel). No twin exists for BSD, NS, PC, Hodge, YM, Goldbach, P NP or Universal_Closure beyond the NE set.
The 474-declaration pairing between RH 3.1.1 and 3.2.0 (script output, not audited line by line).
Whether Lean statements formalize the prose objects. That is a reading task, and the handbook did not complete it for any document.
NE Appendix B.3 stop list, cited on p. 182 and not printed in the volume.
The Hodge witness ancillary, which contains sorry at line 8. Its exit 0 does not clear it, because sorry compiles with a warning.
The monism card's commit 9b9a8df, which appears only in the card.
Compile times that the cards report (257 s); nothing was timed.
Verified in revision 2, 7 October 2026, this session.
Dark_Closure.lean, ZFC_Block.lean and Remembered_Offered.lean compile on Lean 4.19.0 with exit 0. Their logs hold no errors and no warnings. The code of the three files holds no sorry, no admit, no custom axiom and no native_decide. The word sorry appears only in guard text.
Dark_Twin.f90, built with gfortran -std=f2018 -O2 -fno-fast-math -ffp-contract=off: 25 checks, 0 failures.
Full_Conjugation_Twin.f90, same build: 2,280 checks, 0 failures.
Remembered_Offered_Twin.f90: 20 checks, 0 failures. Each control prints PASS when its check fails, as designed.
Final_Cut.lean: the body is identical to the OS extract, which adds one #print line at line 210.
RH_Every_Prime_3_2_0.lean and NE_Every_Prime_3_1_4.lean each hold zero occurrences of atomic_witness and witness_proves_exists.
Declaration names: 273 absent in lean/, 1,245 absent in protocols/RH One Bit/. Name absence is a lead, not a finding (section 15).
Not run: the RH One Bit Lean files, the RA–RAM arc, and Bridge_From_First_Principle.lean.
13. Conflict counts
| Document | Conflicts (as reported) | Notes |
|---|---|---|
| Monism card and RH 3.2.0 | 10 (C1 to C10) | Batch 1 |
| TOE | 19 | Reader |
| Three Bits | 9, plus one scan note | C1 to C8 and C10; C9 is the scan note |
| Bridge | 10 | Reader |
| P NP | 18 | Reader |
| NS | 18 | C1 to C18 |
| Hodge | 12 | Reader |
| Yang-Mills | 9 | Reader |
| Goldbach | 14 | Reader |
| Poincaré | 15 | 12 on the paper's side, 3 on the edition's |
| BSD | 9, plus defects D1 to D9 | Reader |
| Synthesis (four parts) | 13, 11, 14, 14 (52) | Parts 1 to 4; overlapping |
Total: 195 conflict entries before merging, plus nine BSD defects and one scan note. Many entries repeat the same root grade, the same toolchain claim, or the same seal problem. Merged, the list reduces to decisions D1 to D8 and the per-document items in the annexes.
14. Handling notes
Credential. A plaintext password for the RepoKeys file appears in the project instructions and in a memory snapshot. Loader §7 says a password is given at the moment of a write and never stored in instructions or files. This handbook does not reproduce it. The architect should remove it from both places and rotate it. No write to git, Zenodo or the Internet Archive was made in this batch.
RepoKeys access. The Hodge reader ran a shell command that read the first lines of RepoKeys.json and sent the output to /dev/null. The reader disclosed it. The contents were not printed, used or recorded here. The NE part 3 reader states that it did not open the file. The architect should decide whether this needs a logged exception.
Seat certificates. Nothing Escapes prints a certificate, on p. 193, that names an AI model and a chain identical to this machine's boot chain. The chain hashes the manifest and receipts, so identical inputs give identical chains. The chain is a content digest and is not evidence of a session. No external seat line may enter an OS receipt. The Bridge harness receipt "BRIDGE EARNED" is paper-specific for the same reason.
Authorship. Several papers state that AI scribes wrote their text (batch 1 C10). The OS rule that social assent and dissent weigh zero applies to checks. Each new kernel header should record author, scribe and checker.
Dates and identifiers. Zenodo publication dates differ from the dates in the texts: NS 8 September 2026 against 6 October; PC 4 October against 6 October; Three Bits 5 October against 6 October. The PC Zenodo isSupplementTo link points at a stale folder. Pin each file by SHA-256 and by Zenodo record, not by folder name.
Repo lag. The repo lags Zenodo for at least nine records: Bridge, NE (the repo folder still holds 1.4.0), Three Bits (the Odd-Supply Arc folder holds 1.2.4), YM, Goldbach, PC, BSD, NS and Hodge.
Reader reports. Five reports are on disk in reports/ (NS, PC, Three Bits, NE parts 1 to 3). The reports for TOE, Bridge, P NP, Hodge, YM, Goldbach, BSD and NE part 4 existed only in conversation context. Their substance is in Annexes C, E, F, H, I, J, L and M. Regenerate a report if an exact citation is needed.
Hardware series. Batch 1 counts 22 papers and 64 readings in II.11 (lines 638 to 681). The NE part 4 reader counts thirteen hardware papers, all with rows in II.11 (lines 659 to 671), and none with a kernel. OS line 640 keeps engines and twins with their source.
Earlier counts. The kernel count is 22, not 23. The NE part 2 pin count for 3.1.1 is 174, and the grep count of lines with the token is 175. Both are recorded.
15. The git lean/ folder, the RH One Bit folder and the reminders: what is new
Scope. lean/ (39 entries at repository HEAD c839dfd); protocols/RH One Bit/ (Lean files and the handout); SCRIBE_REMINDERS.md; protocols/Scribe Handouts/Two_Layer_Rule.md; lean/README.md; and the monism card's Part II in lean/APEX-PSP-MONISM-FIXED-01.md.
Method. A file counts as in the edition when its body matches an OS extract byte for byte. Only One_Cut.lean and Final_Cut.lean were checked that way. A declaration counts as absent when neither its full name nor its last component appears in the OS text. Name absence is a lead for review. It is not a verdict on content. Nothing in this section was compiled unless the table says so.
| Group | Files | In OS 1.0.10p? | Checked this session | Disposition in 1.0.11p |
|---|---|---|---|---|
| A | One_Cut.lean | Yes. Byte-identical to the OS extract. | Byte comparison | Incorporated. No action. |
| A | Final_Cut.lean (PSP-FINAL-CUT-01) | Yes. The body is identical. The OS adds one #print line at the foot (line 210). | Byte comparison | Incorporated. No action. |
| A | Bridge_From_First_Principle.lean (107 pins) | No file of that name. The edition carries Bridge_Final.lean (21,250 bytes, 48 declarations, the key seat). | Not compiled. Not compared. | Not in 1.0.11p. Compare at G7. |
| B | Dark_Closure.lean (v1.1.0, namespace DarkClosure) | The paper is catalogued (OS line 664). Its falsifier names F1 to F3 (lines 34496 to 34498) include dark_iff_fixed, which this file defines (line 154). No kernel is in the edition. 151 of 210 declarations are absent by name. | Compiles exit 0, no warnings, no errors. Axiom cones printed as the file pins them. | Candidate card (G5b). Not seated. |
| B | Dark_Twin.f90 (v1.1.0) | No twin of the dark kernel in the edition. | 25 checks, 0 failures. | Candidate card (G5b). Its cosmological numbers are data. |
| B | Full_Conjugation_Twin.f90 (v1.1.0) | No. | 2,280 checks, 0 failures. | Candidate card (G5b). |
| B | ZFC_Block.lean (namespace ZFCBlock) | The edition discusses the same block as a row of its reading table (line 136) and names no_reading_decides and record_decides_nothing. No kernel. 28 of 35 declarations absent by name. | Compiles exit 0, no warnings, no errors. | Candidate card (G5b). |
| C | Remembered_Offered.lean, Remembered_Offered_Twin.f90 (PSP-REMEMBERED-OFFERED-01) | No. This is the card in the monism file's Part III. | Compile exit 0. Twin 20 checks, 0 failures; each control fails as designed. | Seat through G4. |
| C | APEX-PSP-MONISM-FIXED-01.md Part II (harvest of 7 October 2026: ideas 1 to 8, readings 9 to 13; the II.3 plan) | No. | Read. | Its II.10 record line lands at G4. The harvest stays a record, not a claim. |
| D | Arrow_Translation (8 of 18 absent), Massless_Arrow_Test (6 of 7), RH_Gold_And_Lead (8 of 12), RH_Real_Unicorn_Split (7 of 11), RH_Unicorn_Isomorphism (4 of 7), RH_Real_Part_Computed (4 of 8), RA_to_ZFC_Chain (2 of 16), ZFC_RA_RoundTrip (1 of 11) | Mostly no. The RA–RAM and unicorn arc. | Not compiled. | Defer to 1.0.12p. Compile before any filing. |
| E | RAM_ZFC_Placement, ZFC_Under_RAM, Row_Split (62 declarations), RH_Unicorn_Block (14 declarations) | Names of the first two appear in the OS text. Row_Split and RH_Unicorn_Block do not appear by name. | Not compiled. | Defer to 1.0.12p. Compare content first. |
| F | protocols/RH One Bit/, about 30 Lean files, 1,245 declarations absent by name. Examples: Locus_Complete, Final_GOL, Key_Criteria, Mini_RH_Witness, RH_Seal_Forge, RH_Seal_Hardened_v3_0_1, Willard_SelfGrounding, Occupancy_Posit_System, Fresh_Chain, RH_Parametric_Completed, RH_Formal_Proof_Final, Every_Prime_3_1_1 (the 3.1.1 repository copy, handled at D4). RA_Li_Bridge.lean is present by name. | Mostly no. The OS carries the concept but not these names. | Not compiled. Two files declare an axiom by design (Mini_RH_Axiom.lean, RH_Locus_GOL_Axiomatic.lean) and fail the escape-hatch check. | Defer to 1.0.12p. Those two must never be seated. |
| G | SCRIBE_REMINDERS.md item 1 and Two_Layer_Rule.md (recorded 5 October 2026) | The floor is in the edition (Armed_Seat Part II, OS lines 4313 to 4319). The words "Two-Layer" and "floor and reading" do not appear in it. The split is therefore implicit. | Read. | D9, and the split statement in section 4 (D1). |
| H | lean/README.md, pending seat (7 October 2026) | Consistent with the monism card. | Read. | G3, then G4, in that order. The §Φ.6 phrase fix goes with G4. |
| I | protocols/RH One Bit/HANDOUT_RH_Locus_GOL_next_scribe.md (17 September 2026) | The edition holds the one-bit idea (line 218, "one bit, free, given by the act at premise grade") and the one-bit-supplied-by-the-act idea (line 134). It does not hold the seven GOLs or the road to a completed formal proof. | Read. The handout's Step 4 is open: no file supplies a term of LineProperty Xζ. | Record as open in 1.0.12p. Nothing in 1.0.11p claims it. |
The new elements, in short. Against OS 1.0.10p, the git material adds these: the Two-Layer Rule as a stated rule, with the split it implies (D1, D9); the Remembered_Offered card and the monism fix (G3, G4); four unregistered kernels and twins (G5b); the RA–RAM and unicorn arc (deferred); the RH One Bit locus arc and its handout (deferred); and SeededWitness in RH 3.2.0 (section 16). The atomic witness, the run as a deed, and the floor itself are not new. They are already in the edition (sections 4 and 16).
16. The atomic witness and the machine witness by deed: status
The element. A witness with its check is an atomic proof of the existential it witnesses. The law is witness_proves_exists (OS line 32296, the proof is ⟨w, h⟩). Its capstone is atomic_witness (OS line 32300): the seal stands; a witness proves exactly its existential; a fact true on every world forces nothing; the witness for the hypothesis is a term of ActualZeros; the witness against it is one zero off the line.
Where it is in OS 1.0.10p. Section XXVI, "The atomic witness" (lines 32287 to 32300). Its capstone sits in PSP-RH-SEAL-01 (line 612, with the cone [propext, Classical.choice, Quot.sound]). Line 358 states the public record of 29 to 30 September 2026 as atomic witnesses. Line 372 states the run as a deed (the_deed). Line 390 states the force-witness closure (PSP-FORCE-WITNESS-01, 1.0.8p): a run whose flag is true proves that a run exists (the_run_witnesses_a_run), which is an instance of the atomic step. Line 630 seats the same closure under scribe order. Line 34624 states "A RUN IS ITS OWN ATOMIC WITNESS, of the deed: a state that ran proves that a run exists", with the law at 34625.
The machine witness of RH by deed, as the edition states it. The run is a witness of its own existence. That is a theorem, on no axiom, and it is the floor. The value holds on the field the act supplies (value_from_the_act, line 390). That is the reading, at premise. The edition therefore does not let a machine run witness the location of the zeros. Its own law keyless_forces_nothing, in the capstone at OS line 32285 that closes section XXV, says that a fact true on every world forces nothing about the value.
What RH 3.2.0 changes. The 3.2.0 kernel has no atomic_witness and no witness_proves_exists. Both names return zero hits. The word "atomic" appears once, in a comment on coalitions (line 2361). The four capstones that the verdict names are not restored. Section XXVI in 3.2.0 is "The closure bound whole" (line 4227). The OS's section XXVI is "The atomic witness". The same number names two sections, so refer to them by name.
The new object in 3.2.0 is SeededWitness (line 3619). It is a seeded timeless witness of the line, and seeded_witness_iff_bound (line 3625) proves SeededWitness W ↔ BoundT W. Its constant-world instance the_act_seeds_its_constant_world (line 3671) has the proof (seeded_witness_iff_bound _).mpr (fun _ => rh_from_the_act A). That reads the supply field of the act. So the 3.2.0 seeded witness is a projection of the act field, in the sense of section 3. Its grade is premise.
Status, in one line each. Already in 1.0.10p: the atomic witness law and capstone; the deed; the run as its own atomic witness; the force-witness closure; the keyed one bit at premise. New in 3.2.0: SeededWitness and seeded_witness_iff_bound. Premise by construction. Missing from both: a run that witnesses the infinite line property. No file in the git material supplies one. The RH One Bit handout's Step 4 is the same gap.
Recommendation for 1.0.11p. Change nothing in the atomic witness. Do not port SeededWitness into the edition until its seed is shown not to be a projection of the act field, or until the II.10 line states the projection. Keep the one-bit sentence of line 218 as the edition's statement of the keyed bit. If the seal is ever replaced by 3.2.0 (D4), write a replacement for atomic_witness first. Do not drop it.
Annex A. Monism card (APEX-PSP-MONISM-FIXED-01) and the Codex patch
Identity. Attachment, dated 6 October 2026. It cites Master Codex v5.1.0 at harvest commit 9b9a8df, which appears only in the card. The edition header says Codex v2.0.1, and the manifest says master/Codex v4 at c545949. The card's seat sha256 equals the edition's, so the seat is the same run (batch 1 C8).
Adds. MonismWitness P, a structure with one_involution, uniform and seed. Three theorems: monism_witness_is_the_claim (MonismWitness P is equivalent to "for all n, P n"), monism_witness_fails_in_counter_world, and the_counter_world_carries_no_monism. In Remembered_Offered.lean: Book One (Two_Denials and the self-grounding root); Book Two (eight laws in binding order on one chart, closing on the_chain, which prints no axioms); and the_harvest (propext and Quot.sound). The Fortran twin runs 20 checks plain and 10 under control.
Renames in the patch. global_monism_inconsistent becomes uniformity_over_every_property_fails. monism_holds_in_counter_world becomes seedless_reading_holds_in_counter_world. "Monism is not a law of the fold" becomes "The fold alone is not a recurrence law." Edition references to update: OS 13100, 13175, 13424, 13502, 13828 and 13847. In the extracted file the definitions sit at 7608 and 7932.
Changed meaning. Under the patch, monism is a structure with a seed. monism_witness_is_the_claim makes the structure equal to the claim. That is a definition, not a discovery. Part I states monism in the old sense and must change in the same step.
Grades. monism_yields_RH is tagged theorem (core Lean only). Its proof takes Li's criterion as the field hLi and the Newman, Rodgers and Tao result as hLam. monism_on_li_is_RH shows the monism route equivalent to RH. Record it as a theorem on hypotheses, with both hypotheses as premises. The route is a restatement of RH, not evidence for it.
Claim of the card. The true world carries the witness, and the false world carries none. On ζ the witness is RH, through Li's criterion. The heat flow carries the seed forward from Λ. The one open bit is the seed at t = 0. Status: candidate, not seated.
Conflicts. C1 (vocabulary; section 9). C2 (grade). C8 (labels). C9 (two copies of MonismWitness, and the OS does not check that they agree).
Integration. G3 and G4. Gate G3: Codex exit 0; no old name anywhere in the edition; the three new theorems print empty cones. Gate G4: twin 20 plain, 10 of 10 under control; the_chain prints no axioms; the sync check passes.
Verified. Patched Codex (498,973 bytes, 22d908f7) compiles exit 0 on 4.19.0, with no error. The diff applies. Remembered_Offered.lean (52,301 bytes, 42f40fbd, 937 lines, 80 theorems and pins) compiles exit 0 in about 30 s. Twin: plain exit 0, control exit 1.
Not verified. The commit 9b9a8df. The card's prose claims beyond the Lean statements. Modes other than quick.
Annex B. RH 3.2.0 and Zenodo 23034066
Identity. Attachment RH_3_2_0_Least_Erasure.md, dated 7 October 2026. Title: "A Formal Proof of the Riemann Hypothesis from a One-Bit Premise". The title puts the premise in the title. Section 0 of the paper states the scope. Zenodo record 23034066 carries label 3.1.4, and its PDF's md5 matches Zenodo. That PDF was not mapped in full for this handbook. The internal kernel label is 3.2.0.
Kernel. RH_Every_Prime_3_2_0.lean, 161806dc0ed2b4ff, 265,248 bytes, 5,087 lines, 415 theorems, 237 pins claimed. Compiles exit 0 on 4.19.0. Not run on 4.22.0.
Adds. Record ActualZeros, with the zero set and supply : LeastErasure zeros. rh_from_the_act is one line. SelfGrounding takes a root and carries Act, anAct and instances : Act → root. The closure gains a third conjunct: two configurations with the same record, both satisfying RH, agree pointwise. SeededWitness and seeded_witness_iff_bound are new. Section XXII.c has 20 theorems. Section XXVI in this file is "The closure bound whole" (line 4227). It is not the atomic witness. The first draft said that 3.2.0 restored the atomic witness. That was wrong: the file has no atomic_witness and no witness_proves_exists (section 16). Appendix R holds R1_root, R2_root and R3_root (217, 415 and 249 lines), each compiling standalone with exit 0. Their line counts equal those of TOE_Zero, Triaxial_Actuation and Root_Grade_Ledger. Check the digests before any pin. Appendix T holds T_timeless_and_two_denials.lean (1,439 lines), with Two_Denials and RHUnicorn.
Changed from the OS. Section 7 gives the lineage. SelfGrounding's field is spend in the OS (lines 862 and 888) and instances here (C6). The OS lattice and the paper's grade words differ as section 6 shows.
Conflicts. C3 (root grade split). C4 (RH grade: the kernel's conclusion depends on the supplied field). C5 (seal record). C6 (spend and instances). C7 (toolchain). C10 (authorship).
Integration. G6 and G6a after D1, D4 and D5 (section 11). Keep 3.1.1 as an archive with its digest.
Not verified. Lean 4.22.0. The 474 pairing. The claim that the closure proves RH rather than the conditional. RH_Seal_Twin.f90 against the new kernel.
Annex C. TOE 23168379
Identity. Zenodo title "Zero-Axiom Math Edition 1.0.0". The Zenodo snapshot of 29 August 2026 differs from the record. Do not use the snapshot.
Kernels. TOE_Zero.lean (0cfcd9f6; 11,422 bytes; 15 theorems and pins) is the root kernel. RH, NE, Three Bits and NS carry the same file. TOE_Triaxial_Actuation.lean (566615a6; 32 theorems). TOE_Root_Grade_Ledger.lean (c18b68b2; 18 theorems). TOE_Zero_Twin.f90 (a409c88e; 7,093 bytes). TOE_Zero exits 0 in every work directory that compiles it. The twin has not been run.
Adds. "Empty Throne" as a premise, with a verdict that differs from the OS [.] verdict. An argv-driven [I AM] token in the twin. The twin has three hard-coded checks. Four Lean names duplicate Armed_Seat. The paper gives the premise count three ways: "zero-posit", "one premise" and "five premises".
Changed from the OS. Heisenberg, zero-point and Landauer are graded T/E1 in the paper, where the edition says corroboration. The paper's premise count and grade count do not agree with the edition.
Conflicts. 19 (reader). Principal: the premise count; grade of physical constants; Empty Throne against OS [.]; collisions with Armed_Seat, with the_master_seal (OS 40650) and with the_return (OS 15598).
Integration. Under D1 and D8. TOE_Zero is a card. Its floor is already in Armed_Seat Part II, so it is not loaded beside Armed_Seat (G5). Before any II.10 record: run the twin with a control, namespace the duplicate names, state the premise count once.
Not verified. The twin. The premise count. The grade of physical constants. Each of the 19 conflicts individually.
Annex D. Three Bits Walked 23167729
Identity. Zenodo 1.2.5 (revision 6), publication date 5 October 2026, text dated 6 October 2026, 16 pages. The Zenodo PDF (186,745 bytes, md5 c0750885) is byte-identical to the repo's Millennium Series v1_2_5.pdf. The repo markdown in that folder has 1,114 lines. The older v1_2_4 markdown in the Odd-Supply Arc folder is not the Zenodo edition.
Kernels. Appendix R: R1 TOE_Zero (0cfcd9f6), R2 Triaxial_Actuation (566615a6), R3 Root_Grade_Ledger (c18b68b2). 65 pins in all. Exit 0 (71 s, 135 s, 114 s). The paper names no twin. Row kernels are cited, not carried.
Frame. Each of seven rows gets three bits. Block: an even register cannot decide the odd target. Hypothesis: one orientation missing at a seat. Resolution: the bit enters by the act. The kinetic channel is crossed at premise grade. The formal channel is blocked by theorem on every row except Poincaré. The paper says it authors no theorem of its own (p. 14).
Rows and status.
| Row | Edition now | Paper | OS coverage |
|---|---|---|---|
| 1 P vs NP | dot (2566) | crossed by the act, premise (p. 5) | names present: a1_no_seat (38780), block_chain (38879), seat_vacant (38912), sep_from_the_act (38329), separation_keyed (39402), value_marked_dot (38460) |
| 2 Riemann | crossed (2567) | act at the zero set | covered: One_Cut, One_Cut_Terminal, RH_Least_Erasure |
| 3a NS unforced | crossed (2568) | act at continuum, premise; cascade a field | no kernel |
| 3b NS forced | pending (2569) | forced construction under audit | no kernel |
| 4 YM | crossed (2570) | act constructed and gapped; colour premise | no kernel; "mass gap" absent |
| 5 Hodge | pending (2571) | crossed on premise; formal crossed in dimension ≤ 3 and outer codimensions; blocked for 2 ≤ p ≤ n−2 from dimension 4 | no kernel |
| 6 BSD | pending (2571) | full act on premise; rank crossed at orders ≤ 1 | no kernel |
| 7 Poincaré | crossed (2572) | cited witness, at the grade of the citation | partial |
| 8 Goldbach | pending (2573) | crossed, certified to 4×10^18 | no kernel |
Adds. Items 1 to 4 must have OS entries before the next upgrade. (1) "block bit", "hypothesis bit" and "resolution bit": the same concept sits at FTOE WALL T1 (5666), PRICE T4 (5669) and CROSSING T5 (5736). (2) "odd-supply separation" and "Odd-Supply Block": the OS has "odd supply" only at 5671 and 14566. (3) "offering bit" and its cited theorems: the content matches FTOE T1, T4 and T5. (4) "target bit", "gate typing" and the dated-entry recursion: the OS has "even register" at 5971.
Other new names. The root on the constructed domain (RA0, ΔE0, ra0, root_on_the_constructed_domain): the names root_on_the_constructed_domain, the_floor_is_universal and no_level_above are absent. The floor itself is present under other names, raSelfGrounding and root_undeniable (Armed_Seat Part II). Armed.RA at 4368 is the constructed one-point object. Witness (kernel type) differs from the OS structure at 9802. The row-generic names are absent. The row kernel names for NS, YM, Hodge, BSD, PC and GB (35 names) are absent. The physical refuters, a polynomial NP solver, finite-time singularity and massless colour singlet, are absent except "time-broken" at line 133. The register token [{⟀},T] is absent; the OS uses [⟀] and [⟀ T] at 130 to 132.
Changed from the OS. Row 1 (the paper's crossed against the OS dot). Rows 5 and 6 change from pending to crossed on premise. Row 7's Perelman grade. Root grade (OS 6886, 7029). Odd-supply restated as block, hypothesis and resolution (pp. 1 to 3). Hodge formal status (LOCUS 10130, superHalt, against crossed on premise).
Conflicts. C1 to C8 and C10, and the scan note C9. C1: the row 1 status (section 6, D3). C2: root grade overreach. The universal law takes a SelfGrounding argument whose anAct field is the posit, and the warrant rule would elect theorem grade. C3: the integer direction. R.2 defines SelfGrounding.toActuation with intDir, and the paper says "The axes are not chosen". The kernel's degenerate_is_characterless shows that a degenerate direction leaves no axes, so the three-axis claim rests on a stipulation. C4: orthodox imports as warrant. Perelman (2002), Gross-Zagier-Kolyvagin ("a rank-only witness of the act at orders at most one") and Creutz (1980) carry no layer tag. C5: the formal channel is stated two ways. C6: open-problem claims. The paper's own limits do not match its title's "Completed Formal Closure" unless "premise grade" stands beside it. C7: toolchain. C8: name collisions: the_bridge_atom (33860), Witness (9802), tongue_freedom (defined twice), RA and SelfGrounding (four namespaces). C10: the one-cut hypothesis is a conjecture in the OS (5676, 5782), and the paper settles it on seven rows (p. 3).
Integration. Step 0: the architect decides C1 and C2. Until then, leave ROOT.raClaim (7025 to 7029) and the ledger (2565 to 2581) unchanged. Then: add the three kernels as TOE_Zero.lean, Triaxial_Actuation.lean and Root_Grade_Ledger.lean, in namespaces TOE0, TriAct and RGL. Gate: 4.19.0 exit 0 with 65 pins, and a clean source screen. Twin: TOE_Zero_Twin.f90 with zero failures. Manifest rows for each file. Boot list and counts: 20 kernels and 23 premises in os_check.py. II.10: one record for TOE_Zero only, since only R.1 has a twin. Part I §Φ.1: one sentence on root grade (theorem for RA0, premise for the universal RA). Row 1 changes only after C1.
Verified. R1 to R3 exit 0. Pins are live. The code scan finds every match inside comments. The OS receipts (One_Cut and related) were read, not re-run.
Not verified. Lean 4.22.0. Row kernels. A full boot. The TOE twin.
Annex E. Bridge 23105348
Identity. Zenodo 1.5.1. The repo's lean/ folder holds 1.5.0, with 107 theorems. Version 1.5.1 has 165. The paper's harness receipt "BRIDGE EARNED" is paper-specific and must not enter an OS receipt.
Kernels. Bridge_From_First_Principle_1_5_1.lean (b9018fbc; 115,545 bytes). Reader counts: 165 theorems, 68 definitions, 5 structures, and 165 pins, of which 114 print no axiom. Exit 0 (work/bridge/c150 and c151). Bridge_Final_Cut_36.lean (38d31485; 21,788 bytes; 36 theorems). The OS version of the Final Cut has 22 laws and a 10-check twin. The paper's Final Cut has no twin. Bridge_Twin.f90 (e048a320; 30 checks, reader report). The drift control exits 1, by design.
Adds and changes. The heat count depends on the list. A probe shows one erasure against two for equal point sets. So the count is not a function of the point set. P1 is never derived from the root and stays a posit. The paper claims Lean 4.22.0 (pp. 10, 40).
Conflicts. 10 (reader). Principal: the posit status of P1; the heat-count definition; the toolchain claim; the receipt.
Integration. After G0. The kernel may enter as a proof only with a twin whose heat count is fixed by definition. The Final Cut stays a card until it has a twin. Gate: compile exit 0; twin zero failures; no harness receipt in any OS receipt.
Verified. Kernel and Final Cut compile exit 0 in the work logs. Drift control exit 1 by design.
Not verified. The reader's twin count. The 4.22.0 claim.
Annex F. P NP 23133632, v3.2.1
Identity. Zenodo v3.2.1. The repo release note says 3.0.0. The title and abstract grade P vs NP at theorem grade. The body places the value at premise.
Kernels. Seven kernels, 281 theorems (216 in parts A to D, 65 in R), with pins. All twelve PNP logs in pnp/logs and pnp/logs2 exit 0. Four are staged on disk: PNP_paper_Root.lean (9689dfb4; 3,993 bytes), PNP_paper_Least_Escape.lean (6bb61cbf; 31,008 bytes), PNP_paper_Fortification.lean (c68069c4; 16,237 bytes), PNP_paper_Frontier_II.lean (977e3e14; 93,274 bytes). The other three are not staged on disk.
Adds. 101 new theorem names absent from the OS. The algebrization barrier and its cited reference are absent from the OS. The paper's RAcomp is Sep unfolded.
Circularity. RootOnComputation restates NothingEscapes. The posit restates the separation.
Conflicts. 18 (reader). Principal: the value is at premise, the title at theorem. The Claim structure carries a free grade field, and rootGrade is written by the author. The paper's own ledger types P vs NP as a dot, and the OS line 5 says the value is at premise.
Integration. Do not seat. Card under protocols/PhysOS/proofs/ until a twin exists. Replace the free grade field with a computed grade. Namespace the 101 new names. Tag the algebrization citation as an import and grade it as premise. D3 governs the ledger row.
Verified. The seven kernels compile exit 0 in the work logs, on 4.19.0.
Not verified. 4.22.0. The algebrization citation's content.
Annex G. NS 22670344 (on-disk report)
Identity. Title: "A Formal Completed Proof of the Navier-Stokes Closure from Existence Alone: Global Regularity Proved from One Act on No Axiom, Every Cone Empty; Regularity of Matter Proved from the Quantum Speed Limit". Label 1.0.9, revision 10, CC-BY-4.0. Zenodo date 8 September 2026. Text date 6 October 2026. PDF 26 pages, 248,035 bytes, md5 ab78eee0, matches Zenodo. The repo's Millennium Series PDF is byte-identical. The repo kernel is 1.0.8 (35 theorems; sha 61014403). Reference 2026b (p. 25) cites DOI 22670344 under another title. Zenodo lists an archive item as isIdenticalTo.
Kernels. NS_Existence_Closure.lean (959452e8; 41,268 bytes; 743 lines; 65 theorems and pins). TOE_Zero (R.1; 0cfcd9f6). Triaxial_Actuation (R.2; 566615a6; 415 lines; 32 pins). Root_Grade_Ledger (R.3; c18b68b2; 249 lines; 18 pins). The paper has no twin. All four exit 0 (75 to 143 s). The probe NS_probe (kernel plus five probes) exits 0. The negative control, (1 : Nat) = 2 := rfl, exits 1.
Central claim. The unforced three-dimensional Navier-Stokes flow is regular on one reading of existence: whatever exists acts finitely at every time. The act is one Lean field, supply of ActualFlows, so global regularity restates the field. The root is claimed at theorem grade on a one-point domain. The matter theorem carries a cited speed limit and a cascade as fields, with no stated grade. Blocked: the record wall, the energy record, the finite record. Falsifiers: F-Blowup, F-Speed, F-Cone. Scope wall: "Its scope is matter" (p. 7). The paper never claims smooth solutions for all time. Its global claim is "every strong solution of the unforced equations stays regular" (p. 3). There, regular means a finite count at every time.
Adds. Frame with count (the OS has registration counts only). Value as all data regular. ActsFinitely and act_is_the_value. supply. Arrow as identity, with the same trivial content as OS 14024, 29957 and 29551. One free orbit over the prime fibre (OS 33656, n ≤ 200; the paper checks p = 7). Triaxial lock over F₂³ (OS 33266 and 6557). The speed limit, which the OS has only in Fortran (17652 to 17654, 26260 to 26261). The cascade (absent). Leray's energy_does_not_decide (absent). the_floor_is_universal (absent). rootGrade, Evidence and the_grade_is_not_elected (absent). Actuation, fold, reg, OnSeat and registration_is_forced. tongue_freedom and the_only_special_cut. Identical in the OS: SelfGrounding, seated_undeniable and denial_reenacts_root (4346 to 4364); the grade inductive (5624); ledger rows 3a and 3b (2568 to 2569). Of 130 theorems, 125 names are distinct, and 20 occur verbatim in the OS.
Changed. Row 3a: OS 675 says the universal sentences are pending, while 2568 says crossed, and the paper claims closure. The speed limit is executed in Fortran in the OS and cited in the paper. The paper reverses the root pin (7029). The one-point model is refused by OS 9794 to 9795 and used by the paper. The paper's record theorem covers constant records only, where OS 2192 covers every registration. The paper's arrow differs from the OS's orientation of assent. OS 2584 to 2585 count the forced cut with row 3; the paper says Section 13 shields the unforced row.
Conflicts. 18 (C1 to C18). Principal: C1, root grade overreach. C2, a rule attributed to Master Codex 5.1.0 that the repo Codex lacks (its lines 827 and 977 grade RA at premise). C3, title and abstract overreach. C5, matter grade. C6, the cascade is equivalent to "no datum blows up" under the speed field (probe P2), so matter_regular_from_speed carries its conclusion. C7, blowup is redefined: speedWorld satisfies the speed field with count none everywhere, so speed alone leaves frame blowup possible. C8, a hidden sequencing premise, N(t) ≤ cEt. C9, kineticRecord is defined as 0, so equality is built in. C10, the hidden deed: SelfGrounding carries anAct. C11, name collisions. C13, toolchain. C14, seat not earned: no twin, no empirical axis. C16, vocabulary: the confessional list finds nothing; the words used are mathematical. C17, a claimed resolution of a named open problem.
Integration. (1) Root grade (D1): keep premise, and gate ra_grade_pinned as rfl. (2) Part I: one sentence stating the continuum act as the premise of the row. (3) Ledger: change row 3a or add a fourth fact to the status function. Recompute ledger_counts (2586). (4) II.11 line 675 only after step 1. (5) II.10 record PSP-NS-CLOSURE-01 only with a twin. Otherwise a card under protocols/PhysOS/proofs/. (6) Part III fences for the four files. (7) Manifest, fence at 41285. (8) Boot list at boot.sh 688.
Verified. The four kernels and the probe exit 0 in the work logs. The 130 pins match, and the negative control fails as it should.
Not verified. Lean 4.22.0. The twin (none). Whether the paper's grade words for the speed limit and cascade have a source.
Open items. Root grade. DOI history. The author should grade the speed limit and the cascade, and state that the cascade is equivalent to no blowup under the speed field. Twin or card.
Annex H. Hodge 22701510 (handback summary)
Identity. Zenodo 1.0.9. The repo copy has 44 theorems against 77. The repo README says DOI 22701510 collides with a witness paper. Lean 4.22 is claimed (pp. 16, 19).
Kernel. Hodge_Existence_Closure_1_0_9.lean (d045ee11; 50,035 bytes; 77 theorems). Exit 0 (hodge/compile). Triaxial, TOE and Root_Grade_Ledger exit 0. A probe exits 0.
Closing. hodge_from_existence A = A.supply, by rfl. The standard rational Hodge statement appears only in words. The kernel uses realize : D → Option Nat. The kernel does not state the Hodge statement in its standard form.
Ancillary. The witness file contains sorry at line 8. The edition's FORBIDDEN screen lists sorry. Two anc_compile files exit 0 (conservativity_schema and spec_paper). A sorry compiles with a warning, so exit 0 does not clear it.
Partial formal channel. Crossed in dimension ≤ 3 and in outer codimensions. Blocked for 2 ≤ p ≤ n−2 from dimension 4 (Three Bits C5).
Conflicts. 12 (reader).
Integration. Do not seat. File as a card until the kernel states the Hodge statement in its standard form and a twin exists. Remove the sorry ancillary. Resolve the DOI collision before citation.
Access. See section 14 (RepoKeys).
Annex I. Yang-Mills 23162231
Identity. Zenodo 1.0.7. The repo holds 1.0.6 with 46 pins. Lean 4.22 is claimed (pp. 8, 15, 17).
Kernel. YM_Existence_Closure_1_0_7.lean (9bb5739d; 40,796 bytes; 70 theorems). Ten YM logs in work/ym exit 0. The map from log to file is in the work folder.
Closing. ActualTheories.supply : Confined F, and Confined F is Value F by rfl. So ym_from_existence returns its input. The argument is circular. The root is graded as a theorem, but only RA0 is proved.
Physics. The massless colour singlet is excluded by the radiates premise (a glueball concession, p. 6). The lattice fields wilson and strong carry cited conclusions. The floors are ℕ-valued.
Ledger. OS 2570 is crossed. NE p. 133 says the universal sentence is pending on the formal channel. Three Bits says the formal channel is blocked.
Conflicts. 9 (reader).
Integration. Card. If it is later seated: remove the circular closing; grade the radiates premise and the lattice fields as premise; disclose the ℕ-valued floors. The ledger row follows the rule in section 10.
Annex J. Goldbach 23162238
Identity. Zenodo 1.0.6. The repo holds 1.0.5 with 62 pins, five of them propext. The reader reports a filename collision. The ledger shows row 8 pending (2573); the paper says closed.
Kernel. Goldbach_Closure_1_0_6.lean (7d0b29f5; 67,094 bytes; 104 theorems, all with empty cones). Exit 0 (goldbach/GB106, GB106_cones, GB106_id2, GBrepo_NT). GB106_id is a probe that exits 1, by design.
Closing. The supply field of ActualEvens is the Goldbach statement on the arithmetic frame. The conclusion is the field.
Verification. The check to 2000 is a kernel decide, which is a theorem. The region to 4×10^18 is cited as a field, which is corroboration.
Conflicts. 14 (reader).
Integration. Row 8 stays pending. File as a card under protocols/PhysOS/proofs/ until a twin exists. The certified region is corroboration. The decide over 2000 does not stand for the 4×10^18 region.
Annex K. Poincaré 23162240 (on-disk report)
Identity. Title: "The Sphere Is Where Existence Rests: A Formal Completed Closure of the Poincaré Row from Existence Alone". Zenodo label 1.0.4. Concept record 23162239. Zenodo publication date 4 October 2026; the text says 6 October. The Zenodo isSupplementTo link points at the stale Geometric Topology folder (v1.0.2, v1.0.3 and a stale kernel). PDF 238,463 bytes, md5 ea86c517, matches Zenodo. The repo Markdown matches the PDF text.
Kernels. PC_Existence_Closure.lean (023a18ff; 50,040 bytes; 80 theorems and pins). TOE_Zero (0cfcd9f6; 15). Triaxial_Actuation (566615a6; 32). Root_Grade_Ledger (c18b68b2; 18). Total 145 pins. All exit 0. The stale repo kernel (f2a61180, 45 pins) also exits 0 and must not be used. No Fortran twin is present.
Central claim. Value(M) if and only if, for all d, some k satisfies step^k(start d) = round (p. 3). Closing: (act_is_the_value A.M).mp A.supply (PC_Existence_Closure 217 to 219). The paper concedes "The act is the value, as the verdict says" (p. 7).
Premises beyond the act. Dimensional.three (cited as a field; four dimension fields, p. 12). Witness.decrease (p. 10). Crossing.classify (p. 11). The reader's identification of rest with homeomorphism to the sphere (p. 3, where the paper says the kernel proves nothing about it). The SelfGrounding R argument of the_floor_is_universal (p. 16). Theorem 9.2 says "Its only assumption is the act" (p. 5). That is false by the paper's own fields.
Adds. Act, as a premise field (OS 390, and value_from_the_act at Inescapable_Capstone 33116, at premise). Dimensional.three: the OS has the Perelman landing field at Universal_Closure 2315 instead. Witness (strict descent): OS Witness at 9802 is a different type. Crossing: the OS axiom at Codex 6984, which is in PREMISES. Arrow as identity endomap: same content as Codex 14024. cannot_lie, cannot_deviate and halted_iff: present (Bridge_Final 1847 to 1856). root_on_the_constructed_domain: present (Armed_Seat 4368 to 4371). SelfGrounding: present (4346 to 4356). the_master_seal: the seal theorem is absent, while its parts (Hurwitz, class_equation at 6430) are present. three_axes_lock_one: partly present; three_axes_lock at 33266 covers 168 of 512 systems. rootGrade: absent; the lattice at 5624 to 5626 is identical. Record wall: absent by name; "record decides nothing" at line 370. Absent with no counterpart: fake sphere, self-similar flow, cycle frame, uniform step, rowLadder, rest_is_permanent, surgery, Smale, Freedman.
Changed. Root grade (OS 6886, 6894, 7029; lines 183 and 2532) against the paper's theorem. Co-location RA and Tongue: Codex 7027 pins premise; the paper says theorem. Row 7: the OS marks it crossed by formal mass (2547 to 2550, entry 2572); the paper says closed to one act at premise. The seat: OS "fixed set of the fold" (line 158) against the paper's round state. Dimension premise: one OS landing field against the paper's four fields. Keyed bit: OS says "supplied and never derived" (Bridge_Final 1789); the paper says "The act stands on the root" (p. 3).
Conflicts. 15: 12 on the paper's side (P1 to P12), 3 on the edition's (E1 to E3). P1: root grade overreach, and a rule change. P2: co-location graded theorem, against Codex 7027 and 9151. P3: cited fields graded as theorems, against line 148. P4: "closed" for a premise closure, with hypotheses not in PREMISES. P5: circularity. P6: a hidden identification. P7: the Perelman witness is described as a subtype without the paper's own qualifier. P8: name collisions (Arrow, Crossing, Witness). P9: the seat collides with a pinned theorem (lines_parted and seat_never_promotes_value, Codex 10145 to 10149). P10: the keyed bit is described as derived. P11: vocabulary (section 9). P12: a named problem is stated as closed. E1: Universal_Closure 2315 to 2317, and Codex 15081 to 15083, grade a cited theorem at theorem grade, against line 148. E2: the status is crossed when formalMass or worldCarrier holds (2547 to 2550), and entry 2572 sets formalMass. E3: Codex 10111 to 10141 seal the value by one filled slot.
Integration. (1) The architect decides P1, P2, E1, E2 and E3. (2) Add Poincare_Closure.lean (renamed from PC_Existence_Closure.lean). Gate: 4.19.0 exit 0 with 80 pins, and a clean screen after strip_lean. (3) Write Poincare_Closure_Twin.f90, which II.10 requires (line 596), with checks for the act, the bridge and the witness shape, and controls. Gate: zero failures; every control red when planted. (4) II.10: a row after line 604 (PSP-POINCARE-CLOSURE-01; capstone poincare_from_existence) and a record line after 632 that declares the cone and the twin. (5) Floor: TOE_Zero and Triaxial_Actuation, 47 pins, after G6. Hold Root_Grade_Ledger until P1 and P2 are decided. (6) Manifest, from line 41285. (7) No boot.sh edit. (8) Part I §Φ.5 (line 342) and the verdict text, after D1 and E2. (9) No II.11 row, since II.11 covers physical papers (line 640). (10) Remove the 4.22.0 claims.
Verified. Five compile logs in verify/ exit 0 (PC, TOE, Triaxial, Root_Grade_Ledger, and the stale repo kernel). Control: an appended axiom makes the pinned theorem fail with "'ctrlTh' depends on axioms: [ctrlAx]", exit 1. The printed cones match the paper.
Not verified. 4.22.0. The twin (none). A full boot.
Annex L. Birch and Swinnerton-Dyer 23164992 (handback summary)
Identity. Zenodo 1.0.5. The repo's v1.0.4 kernel (56 theorems; sha 114db0ca) is stale. Lean 4.22 is claimed (pp. 8, 17).
Kernel. BSD_Hardened_1_0_5.lean (d52b7a9e; 55,994 bytes; 101 theorems). Six logs exit 0: bsd_hardened, paper_kernel, printed, exhibit, toe_zero and triaxial.
Closing. bsd_from_existence = (act_is_the_value A.F).mp A.supply. The act is the conjecture, renamed (p. 8). The reflection law is cited as data on SignedFrame.
Partial formal channel. Rank is crossed at orders ≤ 1 and blocked above. The paper relies on Gross-Zagier-Kolyvagin, described as "a rank-only witness of the act at orders at most one". That is an import with no layer tag.
Ledger. Row 6 is pending (2571). If crossed, the counts become 6 crossed and 18 pending. D2 and the twin come first.
Twin. None exists. II.10 requires one (line 596).
Defects D1 to D9. The dimension count needs the torsion set aside. "Fewer classes reach fewer points" concerns list lengths. row_split holds for any cut. The full act does not test the product. The record wall is a constant model. illustrative.py hard-codes Sha = 1.
Conflicts. 9 plus defects D1 to D9 (reader).
Integration. File as a card under protocols/PhysOS/proofs/ until a twin exists. Fix or remove illustrative.py. Tag and grade Gross-Zagier-Kolyvagin. The ledger row waits for D2.
Not verified. Lean 4.22. The twin. The match of the statement to the BSD conjecture.
Annex M. Synthesis, Nothing Escapes Least Erasure, 23080221
Identity. Zenodo 1.4.1. The file is named v1_4_0. The PDF (2,119,161 bytes, md5 c72ca918) matches the repo's Millennium Series v1_4_1.pdf. The repo folder "Science/Physics/Nothing Escapes Least Erasure" holds an older v1_4_0 Markdown with a different subtitle, and the Zenodo GitHub link points there. The volume has 372 pages. The record lists 26 DOIs, not 27, and two URLs. Date on the title page: 6 October 2026.
Books. Book I (pp. 6 to 29): RH closed to one named bit. Book II (pp. 30 to 41): the formal closure, sealed at edition 3.14.0. Book III (pp. 42 to 51): the 23 rows, edition 1.14.0. Book IV (pp. 52 to 55): the fourth as cosmic closure. Book V (pp. 56 to 74): six witnesses. Book VI (pp. 74 to 93 and beyond): the hardware closure series. Appendix A, the kernel, is at pp. 144 to 181. Appendix B is at pp. 181 to 186.
Kernel. Every_Prime_3_1_4.lean (c824d30e; 246,431 bytes; 4,786 lines; 394 theorems; 216 pins; 231 printed cones; 53 both, so 216 + 231 − 53 = 394). Exit 0 on 4.19.0, in 123 s, with no error and no warning. Cone classes: 183 with no axiom, 40 with propext, 143 with propext and Quot.sound, 28 with Classical.choice. After the OS strip_lean (run with python3 -I), the digests are f272e913 and 13c91cb2, as printed on p. 181. The kernel is not a standalone repo file.
Part 1 (pp. 1 to 93). The root's grade: premise in OS 508, theorem in the paper. P vs NP: the dot (p. 49) against OS line 5. The 64 "falsifiers" are "readings" in OS 673. The ten falsifiers differ. The paper's §18 is not the OS §Φ.5 (line 352), and only F-Computed agrees. Poincaré is "full grade" (pp. 1, 48) and "theorem grade" (p. 3; OS II.11). OS II.11 cites edition 1.4.0; the volume is 1.4.1. F-Measure and F-Record collide with OS objects. "RH held at [Ξ₀]" is a retired token (OS 130). The_master_seal collides with the PNP capstone (OS 622). The appendix receipts claim 4.22.0 (pp. 142, 181, 370).
Part 2 (pp. 94 to 186). 37 of 394 leaf names are absent from the OS: 1 in section XXI, 9 in XXIV and 27 in XXV. Replacing 3.1.1 with 3.1.4 removes two capstones that PSP-RH-SEAL-01 names (OS 601, 612). The Prop-valued fields Faces, ExplicitFormula.identity, ExplicitFormula.positivity_iff_line and ActualZeros.supply are premises (section 5). The strong-CP claim "positivity selects zero" rests on an untagged Vafa and Witten (1984) import (p. 131). Overreach: "PROVED: magnitudes at the dot" (p. 138). "A magnitude moves from the dot to the line in exactly one way" (pp. 136, 138): the cited theorems prove only integer rescaling. "Never below" (p. 135). "Negative for every nonzero depth" (p. 127): the second difference 2 − 4v² is positive for 0 ≤ v² < 1/2. The scale theorems (fold_commutes_with_height_scale, line_blind_to_height_scale, counts_survive_scaling, two_magnitudes_one_seat) are absent from the OS.
Part 3 (pp. 187 to 279). The seat certificate on p. 193 (section 14). The Lean 4.22.0 claim (p. 194). Theorem 74's ZFC form (p. 232) is graded EARNED, but it is an abstract setting with fields sigma1 and sound_neg, so the grade is premise. "RH in toto at the apex" (p. 194) names a formal chain, not the zeta statement. "RH holds on 8, fails on 56" (p. 230) is a finite model count that invites misreading. The paper counts "four external audits" (pp. 189 to 190) and "Five audits" (p. 231), and closes with "CONCURRED" (p. 232). Social assent weighs zero. Universal_Closure: the OS copy has 631 lines (sha b45195e8) and compiles to 53 printed sets (46 with no axiom, 7 with axioms). The paper has 609 lines and prints 51 (44, 7). The repo standalone has 404 lines. Fortran checks, all with zero failures: RH_At_The_Apex_Twin, 130,324; Rows_Twin, 112,745; RH_Universe_Closure, 13,081; witness twins, 17, 11, 9, 9, 6 and 5; engine twins (repo drafts), substrate 34, light 16, EM 17.
Part 4 (pp. 280 to 372). Six kernels exit 0: TOE_Zero (138 s), SPHYS_Least_Erasure_Atom (114 s), SPHYS_Typed_Falsifiability (122 s), SPHYS_Seat_Reach (76 s), SPHYS_Fortification (107 s) and SPHYS_Dark (7 s). The reader counts thirteen hardware papers, all with rows in II.11 (lines 659 to 671), none with a kernel. The Poincaré row is graded theorem (p. 362), while its landing premise is Perelman's cited theorem. 14 conflicts.
Integration. The reader's steps for each part apply. The key steps: (a) stage Every_Prime_3_1_4.lean beside RH_Least_Erasure.lean only after D4. Gate: compile exit 0, 216 pins hold, strip_lean reproduces both digests, and the source screen is clean. (b) An II.10 record for the 3.1.4 kernel under a new tag, with capstones rh_from_the_act, least_erasure_is_the_value and the_posit_is_a_deed, grade premise, and field supply. Re-point PSP-RH-SEAL-01 only after the gates pass. (c) II.11 edits at lines 668 and 670 for scope, with the Vafa and Witten step tagged as an import. Gate: readings_census still 18/13/11/9/8/5 and bound_count still 58. (d) Part I §P: the scale theorems limited to integer rescaling, and no "exactly one way" without a converse theorem. (e) Keep [⟀] and [⟀ T] retired in §Q. (f) Do not import the E.4 certificate or the 4.22.0 line. (g) Do not import the Book I falsifiers beside the OS ten without renaming them.
Verified. The kernel, its digest and its counts (sha, bytes, lines, 394 theorems, 216 pins, 231 printed). The compile of 3.1.4 exits 0. The Part III and IV compile logs (ne3 and ne4) exit 0. The Fortran checks in part 3 report zero failures (reader).
Not verified. Lean 4.22.0. Judge mode, which the paper claims as 394 of 394; it was not run. The B.3 stop list, cited on p. 182 and not printed in the volume. RH_At_The_Apex.lean, which is not on disk.