Pith Number

pith:KCCAFQAN

pith:2017:KCCAFQAN2CEZXLMY32K4HUQYKN

not attested not anchored not stored refs pending

Algebraic properties of toric rings of graphs

Augustine O'Keefe, Huy Tai Ha, Selvi Kara

arxiv:1703.08270 v2 · 2017-03-24 · 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{KCCAFQAN2CEZXLMY32K4HUQYKN}

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	2026-07-05T05:01:58.261902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

508402c00dd0899bad98de95c3d218536028957615a4f64282448b34ed5120b2

Aliases

arxiv: 1703.08270 · arxiv_version: 1703.08270v2 · doi: 10.48550/arxiv.1703.08270 · pith_short_12: KCCAFQAN2CEZ · pith_short_16: KCCAFQAN2CEZXLMY · pith_short_8: KCCAFQAN

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/KCCAFQAN2CEZXLMY32K4HUQYKN \
  | 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: 508402c00dd0899bad98de95c3d218536028957615a4f64282448b34ed5120b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c70ed41ca14e424c75cc87509b051855d3d417a2799cbde350e635f7eeb6bad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-03-24T02:50:51Z",
    "title_canon_sha256": "fcb9902c2ef46096c8ba38baff27ab5908bf4e040a5ba77484e654ffed3e0702"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.08270",
    "kind": "arxiv",
    "version": 2
  }
}