Pith Number

pith:K56TUJAN

pith:2025:K56TUJANOGI6NDABRXVY6H5V2R

not attested not anchored not stored refs pending

The GameTheory package for Macaulay2

Chenyang Zhao, Elke Neuhaus, Erin Connelly, Giacomo Maletto, Hannah Tillmann-Morris, Irem Portakal, Vincenzo Galgano, Zhuang He

arxiv:2507.16755 v1 · 2025-07-22 · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K56TUJANOGI6NDABRXVY6H5V2R}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Tropical Degenerations of Network Games:Valuation Classes and Equilibrium Coalescence

Receipt and verification

First computed	2026-07-05T11:41:30.436034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

577d3a240d7191e68c018deb8f1fb5d4505b9e23174a3f271a28266c327efbc4

Aliases

arxiv: 2507.16755 · arxiv_version: 2507.16755v1 · doi: 10.48550/arxiv.2507.16755 · pith_short_12: K56TUJANOGI6 · pith_short_16: K56TUJANOGI6NDAB · pith_short_8: K56TUJAN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/K56TUJANOGI6NDABRXVY6H5V2R \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 577d3a240d7191e68c018deb8f1fb5d4505b9e23174a3f271a28266c327efbc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18fd99c402cbde49b101fe3dc4b25d5e74ab09b83d3b984b070c0b69a3b61176",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-07-22T16:46:20Z",
    "title_canon_sha256": "e2d94aa0419b33057f6c136c9dd9f4179ff85cb1c53c3addd74b8d2cff1f814c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.16755",
    "kind": "arxiv",
    "version": 1
  }
}