Pith Number

pith:7E2XR5SQ

pith:2016:7E2XR5SQRPBZ7CTUKPFCA3WC2B

not attested not anchored not stored refs pending

Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph

Guangjun Zhu

arxiv:1612.08177 v1 · 2016-12-24 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7E2XR5SQRPBZ7CTUKPFCA3WC2B}

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	2026-05-18T00:54:04.328513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f93578f6508bc39f8a7453ca206ec2d050d10a3d3757f903e710932bc7b514f8

Aliases

arxiv: 1612.08177 · arxiv_version: 1612.08177v1 · doi: 10.48550/arxiv.1612.08177 · pith_short_12: 7E2XR5SQRPBZ · pith_short_16: 7E2XR5SQRPBZ7CTU · pith_short_8: 7E2XR5SQ

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/7E2XR5SQRPBZ7CTUKPFCA3WC2B \
  | 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: f93578f6508bc39f8a7453ca206ec2d050d10a3d3757f903e710932bc7b514f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "290aee199d68abd3bcb48d33cd7bebbecd851eab0ebcbc942b0c8a657b7be7ce",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-12-24T13:29:08Z",
    "title_canon_sha256": "ef9fb336898eabbde1e738744ff3092ebd47bc042b65b59ff64cfabbdd282116"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08177",
    "kind": "arxiv",
    "version": 1
  }
}