Pith Number

pith:FALHBMOZ

pith:2017:FALHBMOZBNNAR7VQ7WONBRZXNH

not attested not anchored not stored refs pending

The phases of large networks with edge and triangle constraints

Charles Radin, Kui Ren, Lorenzo Sadun, Richard Kenyon

arxiv:1701.04444 v2 · 2017-01-16 · math.CO · cond-mat.stat-mech · cs.SI · 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{FALHBMOZBNNAR7VQ7WONBRZXNH}

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	2026-05-18T00:32:14.034352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

281670b1d90b5a08feb0fd9cd0c73769c31ac15b9242882ab81ceee1ea7cd4b3

Aliases

arxiv: 1701.04444 · arxiv_version: 1701.04444v2 · doi: 10.48550/arxiv.1701.04444 · pith_short_12: FALHBMOZBNNA · pith_short_16: FALHBMOZBNNAR7VQ · pith_short_8: FALHBMOZ

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/FALHBMOZBNNAR7VQ7WONBRZXNH \
  | 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: 281670b1d90b5a08feb0fd9cd0c73769c31ac15b9242882ab81ceee1ea7cd4b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fca391b55c549936f78ef2871199ba32b8d003571e73a38ed5dfea1be7526c6",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.SI",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-01-16T20:04:14Z",
    "title_canon_sha256": "7d6cc097570b4597d84748e8f6a2282de8b0296f873b1890417d444d46ca3361"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.04444",
    "kind": "arxiv",
    "version": 2
  }
}