Pith Number

pith:SBM4LIPF

pith:2000:SBM4LIPF2PF7QTA4T6NKHV3AE2

not attested not anchored not stored refs pending

A variational principle for domino tilings

Henry Cohn, James Propp, Richard Kenyon

arxiv:math/0008220 v3 · 2000-08-30 · math.CO · 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{SBM4LIPF2PF7QTA4T6NKHV3AE2}

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	2026-05-18T04:00:03.027647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9059c5a1e5d3cbf84c1c9f9aa3d76026a7f6fb8bbaceb381b73f339079cd49e7

Aliases

arxiv: math/0008220 · arxiv_version: math/0008220v3 · doi: 10.48550/arxiv.math/0008220 · pith_short_12: SBM4LIPF2PF7 · pith_short_16: SBM4LIPF2PF7QTA4 · pith_short_8: SBM4LIPF

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/SBM4LIPF2PF7QTA4T6NKHV3AE2 \
  | 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: 9059c5a1e5d3cbf84c1c9f9aa3d76026a7f6fb8bbaceb381b73f339079cd49e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f1a68766c1de2cba9740d3d3496b70962603f03ee1ce5b6fce7c69c57a706ee",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2000-08-30T00:09:42Z",
    "title_canon_sha256": "61ad0a0c14cd63300163959b6a6143103d62881903ef03b58b7e31e7f4e167c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0008220",
    "kind": "arxiv",
    "version": 3
  }
}