Pith Number

pith:NHR7FUKN

pith:2017:NHR7FUKN76KPEWBMWD2GP3BUSX

not attested not anchored not stored refs pending

On the $A_{\alpha}$-characteristic polynomial of a graph

Shunyi Liu, Xiaogang Liu

arxiv:1711.03868 v1 · 2017-11-09 · 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{NHR7FUKN76KPEWBMWD2GP3BUSX}

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	2026-05-17T23:55:43.136120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69e3f2d14dff94f2582cb0f467ec3495f5ad31c128a2e97da4c232b388c772b2

Aliases

arxiv: 1711.03868 · arxiv_version: 1711.03868v1 · doi: 10.48550/arxiv.1711.03868 · pith_short_12: NHR7FUKN76KP · pith_short_16: NHR7FUKN76KPEWBM · pith_short_8: NHR7FUKN

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/NHR7FUKN76KPEWBMWD2GP3BUSX \
  | 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: 69e3f2d14dff94f2582cb0f467ec3495f5ad31c128a2e97da4c232b388c772b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37fb1e3d2ac8b742a0220669eca790f6fd0f09b452d7634d228f551f46c6d9c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-11-09T14:05:01Z",
    "title_canon_sha256": "e0fae8bdf5121a31719769d21581dc780e0c77394727f841de0a4960f8c865d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.03868",
    "kind": "arxiv",
    "version": 1
  }
}