Pith Number

pith:D4XJVYHM

pith:2026:D4XJVYHMC4QWOQ2ZV4NMAGLMZX

not attested not anchored not stored refs pending

Defect Antichains and Multigraded Symbolic Defect Series of Edge Ideals under Graph Blow-ups

Tabinda Rasheed, Wang Yao

arxiv:2606.29817 v1 · 2026-06-29 · 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{D4XJVYHMC4QWOQ2ZV4NMAGLMZX}

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	2026-06-30T02:17:36.604616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f2e9ae0ec1721674359af1ac0196ccde089c0d2ff444e03b09864eb7dcfbc51

Aliases

arxiv: 2606.29817 · arxiv_version: 2606.29817v1 · doi: 10.48550/arxiv.2606.29817 · pith_short_12: D4XJVYHMC4QW · pith_short_16: D4XJVYHMC4QWOQ2Z · pith_short_8: D4XJVYHM

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/D4XJVYHMC4QWOQ2ZV4NMAGLMZX \
  | 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: 1f2e9ae0ec1721674359af1ac0196ccde089c0d2ff444e03b09864eb7dcfbc51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaabd128944d81f9f901eb2b5b712fab6a20b51a26562657c2e3baefe32395b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-06-29T05:51:07Z",
    "title_canon_sha256": "6a0026e085c6eb2ccab438abd48c2268ecb3e56bebb51449a29e9a429f5076aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29817",
    "kind": "arxiv",
    "version": 1
  }
}