Pith Number

pith:M4AZB3IK

pith:2015:M4AZB3IKQSYXHTQMEEIDUJH4R2

not attested not anchored not stored refs pending

Visible lattice points and the chromatic zeta function of a graph

Javier Cilleruelo

arxiv:1507.06967 v2 · 2015-07-24 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M4AZB3IKQSYXHTQMEEIDUJH4R2}

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	2026-05-18T01:25:11.538015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

670190ed0a84b173ce0c21103a24fc8e8b307679111875d1f8f10779cb679926

Aliases

arxiv: 1507.06967 · arxiv_version: 1507.06967v2 · doi: 10.48550/arxiv.1507.06967 · pith_short_12: M4AZB3IKQSYX · pith_short_16: M4AZB3IKQSYXHTQM · pith_short_8: M4AZB3IK

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/M4AZB3IKQSYXHTQMEEIDUJH4R2 \
  | 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: 670190ed0a84b173ce0c21103a24fc8e8b307679111875d1f8f10779cb679926

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d314a65aeca2bea848c144f27ca7dbaa0daec2cac9867453f2b34296c8bd8bcc",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-24T19:19:08Z",
    "title_canon_sha256": "309bbc2ad8ab8cdb7cef0faca5c721e0a799df3dd5b2d4ac81d0bc3fe5fba83d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06967",
    "kind": "arxiv",
    "version": 2
  }
}