Pith Number

pith:V3SJEDH4

pith:2014:V3SJEDH4XOKGFEVB7HJTNOPPGZ

not attested not anchored not stored refs pending

Multipodal Structure and Phase Transitions in Large Constrained Graphs

Charles Radin, Kui Ren, Lorenzo Sadun, Richard Kenyon

arxiv:1405.0599 v3 · 2014-05-03 · math.CO · cs.SI · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V3SJEDH4XOKGFEVB7HJTNOPPGZ}

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	2026-05-18T00:48:43.453632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aee4920cfcbb946292a1f9d336b9ef367d75d85fe9db89546a146a094c0dc1b8

Aliases

arxiv: 1405.0599 · arxiv_version: 1405.0599v3 · doi: 10.48550/arxiv.1405.0599 · pith_short_12: V3SJEDH4XOKG · pith_short_16: V3SJEDH4XOKGFEVB · pith_short_8: V3SJEDH4

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/V3SJEDH4XOKGFEVB7HJTNOPPGZ \
  | 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: aee4920cfcbb946292a1f9d336b9ef367d75d85fe9db89546a146a094c0dc1b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2763afb9d08fc8c9a91e69e77e4d68b42b65ee08e0e0b68c057fc97143852541",
    "cross_cats_sorted": [
      "cs.SI",
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-05-03T15:06:49Z",
    "title_canon_sha256": "2177b674546cad584994278af9e033f1e5aa029b3e1f6b389e677b045977d450"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.0599",
    "kind": "arxiv",
    "version": 3
  }
}