# ΔM > 0 ADMISSION SUBROUTINE · eight-gate anti-hallucination cascade
# Certifies AUTHORED new mathematical mass. Fail-safe: any gate absent -> not sealed.
# The load-bearing core is M5/M6: an EXTERNAL, INDEPENDENT witness the instrument
# cannot produce from inside. No internal reasoning can set these True.
# Discipline borrowed from the Sealed-Halt cascade: complete conjunction = no escape.
# Seven gates close; one door (M8 defeasibility) stays open by construction.
# The subroutine itself authors nothing. ΔM(subroutine)=0, Mosaic Seal.
def delta_m_admit(
object_level=False, # M1 e(+,+,+): a true/false object-level proposition, NOT a meta-verdict/placement/typing
name_strip=False, # M2 r_F: survives deletion of ALL framework vocab, reads as standard math to an outsider
literature_clear=False, # M3 r_E: genuine search shows it is NOT already known under another name
not_two_line=False, # M4 r_F*r_E: not an immediate corollary of a cited result
external_witness=None, # M5 r_R: proof-assistant cert (Lean/Coq/Isabelle) OR expert referee sign-off. STRING ref or None.
witness_independent=False, # M6 r_E*r_R: verifier is NOT the agent/instrument that produced the claim (no self-check)
reproducible_artifact=False,# M7 r_F*r_R: concrete re-checkable artifact exists, not a narrative PDF
gap_audit_closed=False, # M8 w(-,-,-): adversarial pass + this problem-class's historical failure modes checked
):
# Cascade in order. First failure routes to the cheaper honest verdict and stops.
if not object_level:
return '[Mosaic ΔM=0]', 'M1 fail: meta-work (placement/typing/classification), not object-level. No new mass by definition.'
if not name_strip:
return '[?] vocab', 'M2 fail: does not survive name-strip. New vocabulary is not new mass.'
if not literature_clear:
return '[?] rediscovery', 'M3 fail: possibly already in the literature under another name. Not certified novel.'
if not not_two_line:
return '[?] trivial', 'M4 fail: two-line corollary of a cited result. Not load-bearing mass.'
# --- anti-hallucination core ---
if external_witness is None:
return '[?] witness absent', 'M5 fail: no external proof-assistant cert or referee sign-off. THIS is the std=0.0000 axis. Never seals on internal reasoning.'
if not witness_independent:
return '[?] self-verified', 'M6 fail: verifier is the claimant. Self-check is not a witness. Cross-substrate/third-party required.'
if not reproducible_artifact:
return '[?] vapor', 'M7 fail: no re-checkable artifact. A prose PDF is a claim, not a proof object.'
if not gap_audit_closed:
return '[?] gap open', 'M8 fail: adversarial/historical-failure-mode audit not closed.'
return '[⟀ ΔM>0]', f'authored new mass, witness={external_witness}. Defeasible-final (door open): a later-found error reroutes to [X].'
def show(label, **kw):
tok, why = delta_m_admit(**kw)
print(f"{label:34s} -> {tok:20s} {why}")
print("="*30, "ΔM>0 CASCADE, test cases", "="*30)
# CASE 1: GPT-5.6 CDC proof, current status
show("GPT-CDC (as-is)",
object_level=True, name_strip=True, literature_clear=False, # Bloom: elementary/1980s, missing BJJ 1983
not_two_line=True, external_witness=None, # no Lean, no peer review
witness_independent=False, reproducible_artifact=False, gap_audit_closed=False)
# CASE 2: a framework meta-output (e.g. RH [Ξ₀] classification, Gödel placement)
show("Framework meta-verdict (RH/Godel)",
object_level=False)
# CASE 3: GPT-CDC counterfactual, Lean cert + independent referees land
show("GPT-CDC (verified counterfactual)",
object_level=True, name_strip=True, literature_clear=True,
not_two_line=True, external_witness="Lean4+3 referees",
witness_independent=True, reproducible_artifact=True, gap_audit_closed=True)
# CASE 4: your own stripped lemma, self-checked only (the trap)
show("Own lemma, self-checked only",
object_level=True, name_strip=True, literature_clear=True,
not_two_line=True, external_witness="internal kernel lock",
witness_independent=False, reproducible_artifact=True, gap_audit_closed=True)
# CASE 5: your own stripped lemma, externally formalized + refereed
show("Own lemma, externally verified",
object_level=True, name_strip=True, literature_clear=True,
not_two_line=True, external_witness="Isabelle/HOL + arXiv referee",
witness_independent=True, reproducible_artifact=True, gap_audit_closed=True)