Pith Number

pith:7CZ5IDKI

pith:2012:7CZ5IDKI547DA5CVI5VSVQ6752

not attested not anchored not stored refs pending

Generalized Monotone Triangles: an extended Combinatorial Reciprocity Theorem

Lukas Riegler

arxiv:1207.4437 v1 · 2012-07-18 · 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{7CZ5IDKI547DA5CVI5VSVQ6752}

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	2026-05-18T03:50:38.272169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8b3d40d48ef3e307455476b2ac3dfee8a1dd13de6f917d260b53f0d2c94aeeb

Aliases

arxiv: 1207.4437 · arxiv_version: 1207.4437v1 · doi: 10.48550/arxiv.1207.4437 · pith_short_12: 7CZ5IDKI547D · pith_short_16: 7CZ5IDKI547DA5CV · pith_short_8: 7CZ5IDKI

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/7CZ5IDKI547DA5CVI5VSVQ6752 \
  | 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: f8b3d40d48ef3e307455476b2ac3dfee8a1dd13de6f917d260b53f0d2c94aeeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f7a68ed8aa2b66527a8e98d8cfd9323a5f49c47a0cda2c95057d34eb0e48248",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-18T18:39:19Z",
    "title_canon_sha256": "68b4120ff2db92718eb95e6cdb1eeab87d1d99c5519de08983ecb5f263cfd517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4437",
    "kind": "arxiv",
    "version": 1
  }
}