Pith Number

pith:XZCAVZ4J

pith:2011:XZCAVZ4JKRSMJ2ID7ENSOKK7T5

not attested not anchored not stored refs pending

Tropical linear-fractional programming and parametric mean payoff games

Ricardo D. Katz, Sergei Sergeev, Stephane Gaubert

arxiv:1101.3431 v2 · 2011-01-18 · math.MG · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZCAVZ4JKRSMJ2ID7ENSOKK7T5}

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.

Receipt and verification

First computed	2026-05-18T02:22:51.727406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be440ae7895464c4e903f91b27295f9f7fcd0be8f702ac83dc1b81de701f4a36

Aliases

arxiv: 1101.3431 · arxiv_version: 1101.3431v2 · doi: 10.48550/arxiv.1101.3431 · pith_short_12: XZCAVZ4JKRSM · pith_short_16: XZCAVZ4JKRSMJ2ID · pith_short_8: XZCAVZ4J

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/XZCAVZ4JKRSMJ2ID7ENSOKK7T5 \
  | 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: be440ae7895464c4e903f91b27295f9f7fcd0be8f702ac83dc1b81de701f4a36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9fad4fa00a7f85c2d7a48429bd022a59dacb21872952399c885df491c34cb2e",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-01-18T12:03:01Z",
    "title_canon_sha256": "257a3e46daee7e68cfbaee71a556b84a53f1344a50bece37cf748247b25133bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3431",
    "kind": "arxiv",
    "version": 2
  }
}