Pith Number

pith:TCPESGFN

pith:2014:TCPESGFN5IZCVGUFBM4TRUK3UY

not attested not anchored not stored refs pending

A spectral lower bound for the divisorial gonality of metric graphs

Janne Kool, Omid Amini

arxiv:1407.5614 v2 · 2014-07-21 · math.AG · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TCPESGFN5IZCVGUFBM4TRUK3UY}

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	2026-05-18T02:39:23.559253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

989e4918adea322a9a850b3938d15ba634c42ee9a53ed8e907e0fe04bda9b950

Aliases

arxiv: 1407.5614 · arxiv_version: 1407.5614v2 · doi: 10.48550/arxiv.1407.5614 · pith_short_12: TCPESGFN5IZC · pith_short_16: TCPESGFN5IZCVGUF · pith_short_8: TCPESGFN

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/TCPESGFN5IZCVGUFBM4TRUK3UY \
  | 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: 989e4918adea322a9a850b3938d15ba634c42ee9a53ed8e907e0fe04bda9b950

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa7e1e15d8e9eef33db271d6dd0c1b6ff96c2338051c5ca43de4db9edc1369ec",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2014-07-21T19:56:17Z",
    "title_canon_sha256": "8a97c4d701dedcc26785870128aaa22ac15e931fa225d4fa1e88c55692889a29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.5614",
    "kind": "arxiv",
    "version": 2
  }
}