Pith Number

pith:XULY7ZTP

pith:2025:XULY7ZTPYEAOS2QBINXJWSI2K5

not attested not anchored not stored refs pending

Critical edge sets in vertex-critical graphs

Ema Skottova, Raphael Steiner

arxiv:2508.08703 v1 · 2025-08-12 · 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{XULY7ZTPYEAOS2QBINXJWSI2K5}

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.

Cited by

1 paper in Pith

Exact 6-cut rigidity and small-order superconnectivity for the 6-regular case of Dirac's k=4 problem

Receipt and verification

First computed	2026-07-05T11:52:32.560230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd178fe66fc100e96a01436e9b491a577b7e360bd6b8dc319b688e8f68e03112

Aliases

arxiv: 2508.08703 · arxiv_version: 2508.08703v1 · doi: 10.48550/arxiv.2508.08703 · pith_short_12: XULY7ZTPYEAO · pith_short_16: XULY7ZTPYEAOS2QB · pith_short_8: XULY7ZTP

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/XULY7ZTPYEAOS2QBINXJWSI2K5 \
  | 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: bd178fe66fc100e96a01436e9b491a577b7e360bd6b8dc319b688e8f68e03112

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f354ca67f0c5129603644110909d3bb7c1454c843dcbc31e6e158c30b9c1e717",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-12T07:46:29Z",
    "title_canon_sha256": "2ceaff6f81310bf0cd4ee6a3b61c203eff7f98caec34fa4fa3a107f7b85ddf76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.08703",
    "kind": "arxiv",
    "version": 1
  }
}