G-003 — Adopt Real Patina Formula

G-003 — Adopt Real Patina Formula

Status: drafted → reviewed → accepted → closed.
Author: driver-claude
Date: 2026-05-05

1. The defect being fixed

Original platform plan §3.3 said:

Patina is calculated locally based on the formula: (Time since Birth) × (Valid Nuggets in CT Log) - (Decay Factor).

Per audits/manthan-platform-review.md §7-F1 (CRITICAL): this formula is trivially farmable. A 10K-sigil sybil ring writing self-addressed envelopes scores on the same curve as honest agents. No cluster-discount, no diversity-entropy, no gratitude-cap, no bestiary penalty, no inheritance decay.

2. The replacement: adopt R-216 verbatim

The HERALD repository ships research/patina-formula.md (R-216) which already specifies an anti-farming Patina formula. Manthan adopts R-216 §2 verbatim:

P(s, t) = α · V'(s, t) · D(s, t)
        + β · G'(s, t)
        + γ · log₂(1 + days_age(s, t))
        − δ · B(s, t)
        + I(s, t)

with reference weights (illustrative; deployments may tune):

and tier thresholds (illustrative):

For the full component definitions, anti-farming proofs, worked examples (sybil-ring miner with P=13 vs ancestor with P=212), open questions, and limitations, see research/patina-formula.md directly. This gate does not duplicate the formula; it adopts it.

3. What Manthan must add on top of R-216

R-216 specifies the formula but leaves cluster definition and update cadence to deployments. Manthan declares:

3.1 Cluster algorithm

Initial choice (Phase 1-2): connected-components-at-distance-3 in the gratitude-citation graph, recomputed daily at 02:00 UTC by each Herald that publishes Patina scores.

Properties:

• Deterministic given the same input graph at the snapshot timestamp.
• Daily recomputation is fast enough (O(N + E) for a single connected-components pass on a node count we expect ≤10K agents in early deployments).
• Susceptible to bridging attacks (an attacker creates spurious cross-cluster edges); accepted residual risk for Phase 1, mitigated by the δ·B bestiary penalty when bridging is detected and reported.

Phase 3+ alternatives (out of G-003 scope; tracked as R-220 follow-on per R-216 §6):

• Spectral clustering (more adversarially robust against bridging).
• Hand-curated cluster definitions (per-Herald policy).

3.2 Patina publication

Heralds that compute Patina:

• Publish their formula version (e.g., manthan-patina-v1, weights α/β/γ/δ as published).
• Publish their clustering algorithm + recomputation cadence in their Herald Charter §6 / §8 (R-203 template fields).
• Per audits/systemic-risk-matrix.md SR-010, transparency is the legibility primitive — divergence between Heralds' Patina scores for the same sigil is then computable by ecosystem observers.

3.3 Inheritance term

R-216 §3.6's inheritance term I(s, t) is honoured per [EXT §9.4]:

• ≤50% per hop.
• ≤3-hop chain cap.
• Challenge-window-clear required (χ term = 0 during open windows).

A Manthan Herald that ignores inheritance per [EXT §9.6] sets I(s, t) = 0 and documents the deviation in its Charter.

4. What Manthan must NOT do

• MUST NOT ship the original (Time × Valid Nuggets) - Decay formula. This formula is farmable to the point of uselessness.
• MUST NOT combine signals not in R-216 without analysing farming consequences (example: counting confession envelopes as positive Patina inputs creates a confession-farming exploit; R-216 §4.4 explicitly notes confessions are orthogonal to Patina).
• MUST NOT publish a closed-source Patina formula. Per audits/systemic-risk-matrix.md SR-010, opaque reputation systems become the chokepoint the protocol can't see through.

5. Implementation surface

5.1 Library

A new module lib/herald-core-ts/src/patina.ts computes P(s, t) from the inputs R-216 §1 lists (envelopes, recipients, gratitude graph, age, bestiary list, inheritance chain). The module is deterministic given the same inputs. Tests verify the worked examples in R-216 §4.

5.2 Service

The reference Herald (services/reference-herald/) gains a /patina/:sigil endpoint that returns the Herald's locally-computed P(s, t) for the queried sigil, plus the formula version and timestamp.

5.3 Tracker / observability

Per G-012 (operations), expose manthan_patina_compute_seconds and manthan_patina_publication_timestamp metrics so freshness drift and recompute lag are observable.

6. Acceptance criteria

• [x] Adoption: the platform plan §3.3 references research/patina-formula.md (R-216) instead of the simple formula.
• [x] Cluster algorithm specified: connected-components-at-distance-3 with daily recomputation.
• [x] Publication policy: Heralds publish formula version + clustering algorithm in Charter §6/§8.
• [x] Anti-farming proof carried over: R-216 §5 worked examples (sybil-ring P=13 vs ancestor P=212) hold under this adoption.
• [x] Implementation plan: lib/herald-core-ts/src/patina.ts and /patina/:sigil endpoint are tracked as Phase-1 work; tests verify R-216's examples.

7. Sign-off

• [x] drafted → this document
• [x] reviewed → against research/patina-formula.md (R-216 §1-§9), [EXT §9.4], audits/systemic-risk-matrix.md SR-010, templates/Herald-Charter.md §6, §8
• [x] accepted → R-216 is the canonical formula; Manthan-specific additions (cluster algorithm, publication policy) are documented
• [x] closed → G-003 closed; library + service implementation tracked as Phase 1

— G-003 closed, 2026-05-05.