Pith Number

pith:DDCZMK6H

pith:2013:DDCZMK6HD7NG3MSBSVH3T7CF2S

not attested not anchored not stored refs pending

Ergodic optimization, zero temperature limits and the max-plus algebra

A. O. Lopes, A. T. Baraviera, R. Leplaideur

arxiv:1305.2396 v2 · 2013-05-10 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DDCZMK6HD7NG3MSBSVH3T7CF2S}

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	2026-05-18T03:21:45.081524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18c5962bc71fda6db241954fb9fc45d4baf3fcb727ab98271001ea6c18ce8f29

Aliases

arxiv: 1305.2396 · arxiv_version: 1305.2396v2 · doi: 10.48550/arxiv.1305.2396 · pith_short_12: DDCZMK6HD7NG · pith_short_16: DDCZMK6HD7NG3MSB · pith_short_8: DDCZMK6H

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/DDCZMK6HD7NG3MSBSVH3T7CF2S \
  | 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: 18c5962bc71fda6db241954fb9fc45d4baf3fcb727ab98271001ea6c18ce8f29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4767764644906336b3efc8a2a4905b1af47a2a139dde779a546916783e61124a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-05-10T17:53:24Z",
    "title_canon_sha256": "8d4b75f1e7a8add641e8e8623dbe3c0fa904d54f96959f32d99ae5435b4626c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.2396",
    "kind": "arxiv",
    "version": 2
  }
}