Pith Number

pith:WRYJMPLX

pith:2023:WRYJMPLXBTLUIBAGLVDG5FJL7Q

not attested not anchored not stored refs pending

Phase Transitions of Structured Codes of Graphs

Bo Bai, Jie Ma, Yu Gao, Yuze Wu

arxiv:2307.08266 v1 · 2023-07-17 · math.CO · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WRYJMPLXBTLUIBAGLVDG5FJL7Q}

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	2026-07-05T06:31:22.451084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b470963d770cd74404065d466e952bfc397bfefd9b54e40af44f7874b4494401

Aliases

arxiv: 2307.08266 · arxiv_version: 2307.08266v1 · doi: 10.48550/arxiv.2307.08266 · pith_short_12: WRYJMPLXBTLU · pith_short_16: WRYJMPLXBTLUIBAG · pith_short_8: WRYJMPLX

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/WRYJMPLXBTLUIBAGLVDG5FJL7Q \
  | 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: b470963d770cd74404065d466e952bfc397bfefd9b54e40af44f7874b4494401

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f31c664a0fa71091b2b64de77aeea509ef9eadef4a336d2929cc1c9af8a4986",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-07-17T06:15:36Z",
    "title_canon_sha256": "b824f37684aed09f88dd236dee7081119569f75add76791c70b233eff0f53961"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.08266",
    "kind": "arxiv",
    "version": 1
  }
}