Pith Number

pith:YDQGHOQ7

pith:2015:YDQGHOQ7RDQ6J5FEAIW6S43D4L

not attested not anchored not stored refs pending

Bipodal structure in oversaturated random graphs

Charles Radin, Kui Ren, Lorenzo Sadun, Richard Kenyon

arxiv:1509.05370 v1 · 2015-09-17 · math.CO · cs.IT · cs.SI · math-ph · math.IT · 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{YDQGHOQ7RDQ6J5FEAIW6S43D4L}

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	2026-05-18T00:48:43.154228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0e063ba1f88e1e4f4a4022de97363e2cf0a1da39187918cd168ae71eb8a57d5

Aliases

arxiv: 1509.05370 · arxiv_version: 1509.05370v1 · doi: 10.48550/arxiv.1509.05370 · pith_short_12: YDQGHOQ7RDQ6 · pith_short_16: YDQGHOQ7RDQ6J5FE · pith_short_8: YDQGHOQ7

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/YDQGHOQ7RDQ6J5FEAIW6S43D4L \
  | 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: c0e063ba1f88e1e4f4a4022de97363e2cf0a1da39187918cd168ae71eb8a57d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb9f159d7eb3c839a525350701eb35b9e35065f2403ab8fa5180a85022239f1b",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.SI",
      "math-ph",
      "math.IT",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-17T18:47:23Z",
    "title_canon_sha256": "8986c55d79e71dad2b3834e6a6a2cd3f5be9657dd009cf23e1a72954dd3d67ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05370",
    "kind": "arxiv",
    "version": 1
  }
}