Pith Number

pith:OT4KHVTJ

pith:2025:OT4KHVTJYEM45ELFVDRQ6Z6TOU

not attested not anchored not stored refs pending

A short combinatorial proof of Di Francesco's conjecture on Aztec triangles

Mihai Ciucu, Seok Hyun Byun

arxiv:2508.04545 v1 · 2025-08-06 · math.CO · cond-mat.stat-mech · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OT4KHVTJYEM45ELFVDRQ6Z6TOU}

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	2026-07-05T11:49:39.231111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74f8a3d669c119ce9165a8e30f67d3751459212036dcb45c844715ffa7bd5877

Aliases

arxiv: 2508.04545 · arxiv_version: 2508.04545v1 · doi: 10.48550/arxiv.2508.04545 · pith_short_12: OT4KHVTJYEM4 · pith_short_16: OT4KHVTJYEM45ELF · pith_short_8: OT4KHVTJ

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/OT4KHVTJYEM45ELFVDRQ6Z6TOU \
  | 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: 74f8a3d669c119ce9165a8e30f67d3751459212036dcb45c844715ffa7bd5877

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e98a1a52ff72c2b64f639c7f2fcd72a379714d00fb6d436e1f95aba2fdf7986",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-06T15:32:15Z",
    "title_canon_sha256": "e4cef2c55ea4aff1f98c29ea973f48def9da53f650e3536e32c14ede5c682e30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.04545",
    "kind": "arxiv",
    "version": 1
  }
}