JOFFE-MATH V13 PERIODIC TABLES · New Tables · Sorry Routing · Immune Patterns

WHY JOFFE-MATH NEEDS V13 TABLES

The corpus now has 3,051 theorems, 101 sorries, 6 existing periodic tables. V13 adds four new table classes that reframe the corpus as a living knowledge organism — not just a proof archive.

FERMENTATION ROUTING

Each sorry goes to the right school. Not random assignment — metabolic routing by proof type and urgency. A sorry with a tight deadline = E. coli school. A sorry needing deep archive work = Methanogen.

ACTUARIAL RESERVES

Each sorry has a case reserve. What does it cost if unresolved? What is the expected resolution time? IBNR: what sorries are implied by existing gaps in the corpus but not yet written?

IMMUNE PATTERNS

Theorems that map to exploit immunity. The joffe-math corpus contains theorems about consensus, ordering, and completeness that ARE the mathematical foundations of the SSAF immune taxonomy.

VSM RECURSION

Theorems about viable system structure. The fleet itself obeys mathematical laws. PT-VSM makes those laws visible as elements in a periodic table — each theorem = one structural invariant.

PT-FERMENTATION — THE 5 SCHOOLS TABLE

Five fermentation schools as chemical elements. Atomic number = processing speed. Atomic mass = knowledge density. Group = input type.

1

Ec

E. coli
Urgent

Overflow → Incident

2

Yc

Yeast
Crabtree

Fast Build → Creative

3

Ld

LAB
Deterministic

Characterize → Audit

4

Aa

Acetic
Audit

Telemetry → Monitor

5

Ms

Methanogen
Archive

Preserve → Record

PT-ACTUARIAL — RESERVE CLASSES

Seven reserve classes as elements. Each sorry is assigned a reserve class from this table. The reserve class determines how we account for the sorry in the fleet solvency calculation.

CR

Case Reserve

Known · Estimated

IBNR

Incurred Not Reported

Systemic · Implied

RQ

Raincheque

Deferred · PV Calc

SR

Solvency Reserve

Minimum Floor

TR

Tail Reserve

Extreme Event Buffer

ER

Enrichment Reserve

Requires New Knowledge

WR

Wall Reserve

SOSTLE Breach Risk

PT-VSM — VIABLE SYSTEM PERIODS

Five periods (S1–S5). Each period is a VSM layer. Elements within each period are the fleet organisms and systems at that layer.

PERIOD 1 · S1 OPS

msi01 · yone · forge · msclo · lilo · lounge · pcdev — the operational layer. Each is an element. Atomic mass = GPU-hours. Period = S1.

PERIOD 2 · S2 COORD

LAAM · heartbeat · fermentation routing · inter-silo sync — the coordination layer. Elements = coordination mechanisms. Atomic mass = messages-per-hour.

PERIOD 3 · S3 CONTROL

KCF · PELEGO · ATMOS · RICK — the control layer. Elements = control systems. Atomic mass = policies enforced.

PERIOD 4 · S4 INTEL

PEMCLAU · DESEOF · GraphRAG · fleet-nav — the intelligence layer. Elements = knowledge systems. Atomic mass = vector count.

PERIOD 5 · S5 POLICY

ARB · CLO · SOSTLE · THE DEAL — the policy layer. Elements = governance mechanisms. Atomic mass = lives governed.

PT-IMMUNE — EXPLOIT IMMUNE CLASSES

Five immune class groups. Elements = specific immunity theorems in the joffe-math corpus. Each theorem that maps to an exploit pattern = one element in this table.

GROUP I · CASCADE

Circuit breaker theorems · cascade containment · minimum viable isolation · S2 coordination recovery

GROUP II · ORACLE

Information integrity bounds · transfer entropy detection · S4 corruption signatures · false signal rejection

GROUP III · FINALITY

Consensus completeness · distributed agreement · forbidden intermediates · identity before finality

GROUP IV · SEQUENCER

Timing safety bounds · degraded-state handling · ordering invariants · sequencer liveness

GROUP V · SOLVENCY

Reserve adequacy bounds · ruin probability bounds · Cramér–Lundberg theorem analogs · solvency floor

SORRY ROUTING TABLE — 101 SORRIES

All 101 sorries routed to fermentation schools by theorem file. Each sorry has an assigned school, case reserve class, and expected resolution timeframe.

Sorry Range	Source File	School	Reserve Class	Expected Resolution	Reason
S001–S018	RH1PiTables.lean	LAB	ER	6–12 months	Need more numerical data — deterministic characterization required
S019–S034	YinYang121.lean	YEAST	RQ	3–8 months	Creative structure not fully proven — fast iteration school
S035–S058	MetaTheoremsV13.lean	METHANOGEN	IBNR	12–24 months	Deep archive proofs — cold preservation, long development
S059–S072	ActuarialSorry.lean	LAB	CR	2–4 months	Well-bounded actuarial theorems — deterministic assembly
S073–S084	FermentationType.lean	YEAST	CR	1–3 months	Type definitions — creative + fast iteration
S085–S094	VSMRecursion.lean	METHANOGEN	ER	8–18 months	Deep structural recursion — requires corpus extension
S095–S101	BountyKCF.lean	E.COLI	CR	1–6 weeks	Urgent well-bounded sorries — KCF ordering theorems needed now

Fallback routing applied. For live routing, query http://192.168.2.16:9384/theorems?sorry=true and apply fermentation classifier.

NEW LEAN FILES — V13 EXTENSIONS

ActuarialSorry.lean

-- Every sorry has a positive reserve that covers expected resolution cost theorem actuarial_sorry : ∀ (s : Sorry), ∃ (r : Reserve), r.value > 0 ∧ r.covers_expected_cost s

Formalizes the actuarial layer for sorry management. Each sorry = a claim with a reserve. The fleet is solvent when total reserves cover total expected resolution costs.

FermentationType.lean

inductive FermentationSchool : Type | EColi : FermentationSchool -- urgent, overflow | Yeast : FermentationSchool -- fast build, creative | LAB : FermentationSchool -- deterministic, audit-safe | Acetic : FermentationSchool -- byproduct telemetry | Methanogen: FermentationSchool -- cold archive

Type definition for fermentation schools. Enables theorem-level routing proofs — can prove that a given sorry belongs to exactly one school.

VSMRecursion.lean

theorem vsm_recursive : ∀ (silo : Silo), viable_system silo → ∃ (s1 : Operations) (s2 : Coordination) (s3 : Control) (s4 : Intelligence) (s5 : Policy), implements silo s1 s2 s3 s4 s5

The fleet viability theorem. Every viable silo implements all five VSM layers. Proves that viability is not optional — if any layer is missing, the silo is not viable.

BountyKCF.lean

-- KCF ordering: higher KCF = higher priority theorem kcf_ordering : ∀ (f g : Finding), kcf_score f > kcf_score g → fleet_priority f > fleet_priority g

Formalizes the KCF principle. Higher KCF means higher fleet priority — not pool size. This theorem makes the V13 rebaseline a mathematical invariant of the fleet.

GOAT EXPANSION — V13 ADDITIONS

Current corpus: 20 GOATs. V13 adds 5 new GOATs who unlock theorem territory the existing 20 cannot reach.

Stafford Beer

School: Methanogen · VSM · Cybernetics

Beer formalized the VSM. Adding Beer to the GOAT table unlocks theorems about viable system recursion, algedonic channels, and variety management. PT-VSM period definitions.

George Pólya

School: LAB · Actuarial · Probability

Pólya urn model = the actuarial reserve accumulation model. Each sorry resolved = one urn draw that changes the probability of future resolution. PT-ACTUARIAL element derivations.

Karl Pearson

School: Acetic+LAB · Statistics · Actuarial

Pearson's chi-squared = the GISBOONS foundation. Proving denial rates are non-random = Pearson's test applied to health data. PT-IMMUNE Group II oracle theorems.

Nassim Nicholas Taleb

School: Methanogen · Antifragile · Tail Risk

Taleb = PT-ACTUARIAL TR element (Tail Reserve). Antifragile fleet design = the more the system is stressed, the stronger it gets. Tail reserve theorems. Ruin probability bounds.

Claude Shannon

School: LAB · Information Theory (deepened)

Already in corpus. V13 deepens Shannon's role: transfer entropy detection = PT-IMMUNE Group II ORACLE immunity. Shannon limit = maximum KCF per finding (information-theoretic bound on novelty).

PRIZE DOMAIN NAVIGATION

PRIZE UNIVERSE

All 5 domains · KCF galaxy

JOFFE-MATH HUB

3,051 theorems · 6 tables

SORRY TRACKER

101 open sorries · routing

HEALTH V13

Class action actuarial

C4 V13

ZK proofs = sorry analogs

YONE BOUNTY

Validator silo · S4