Pith Number

pith:KIY65XRA

pith:2013:KIY65XRAUJNDHFM5SUYWZZL5SU

not attested not anchored not stored refs pending

Singularities in the entropy of asymptotically large simple graphs

Charles Radin, Lorenzo Sadun

arxiv:1302.3531 v2 · 2013-02-14 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KIY65XRAUJNDHFM5SUYWZZL5SU}

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	2026-05-18T01:34:40.145692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5231eede20a25a33959d95316ce57d9502e1d9094d995dbd10bbbded43a72589

Aliases

arxiv: 1302.3531 · arxiv_version: 1302.3531v2 · doi: 10.48550/arxiv.1302.3531 · pith_short_12: KIY65XRAUJND · pith_short_16: KIY65XRAUJNDHFM5 · pith_short_8: KIY65XRA

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/KIY65XRAUJNDHFM5SUYWZZL5SU \
  | 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: 5231eede20a25a33959d95316ce57d9502e1d9094d995dbd10bbbded43a72589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b43510a2b5304b4ebc5e5a893ad44d0cc093d7149071a880122f358a15a30e2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-14T19:53:13Z",
    "title_canon_sha256": "2b93b01761a89c3b94fcd654a510d9cd1d5e9068cd91edeea2ef6f4e59eca8d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.3531",
    "kind": "arxiv",
    "version": 2
  }
}