Pith Number

pith:DXP37IX4

pith:2021:DXP37IX42W35X3BKATX7WE72XX

not attested not anchored not stored refs pending

Constructions of cospectral graphs with different zero forcing numbers

Aida Abiad, Boris Brimkov, Himanshu Gupta, Jane Breen, Ralihe R. Villagr\'an, Thomas R. Cameron

arxiv:2111.12343 v2 · 2021-11-24 · 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{DXP37IX42W35X3BKATX7WE72XX}

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	2026-07-05T04:16:53.542993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ddfbfa2fcd5b7dbec2a04effb13fabdf2290834ce535212add64c07ae567947

Aliases

arxiv: 2111.12343 · arxiv_version: 2111.12343v2 · doi: 10.48550/arxiv.2111.12343 · pith_short_12: DXP37IX42W35 · pith_short_16: DXP37IX42W35X3BK · pith_short_8: DXP37IX4

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/DXP37IX42W35X3BKATX7WE72XX \
  | 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: 1ddfbfa2fcd5b7dbec2a04effb13fabdf2290834ce535212add64c07ae567947

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bff5b16073b341d3408a90c9e0f099079acdf06dd4e6ed8f79536415c9e648a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-11-24T08:52:02Z",
    "title_canon_sha256": "379e91ecbc90789610369e11adb37aa02fe7056b427b657e7c9d23c1c4cbf34c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.12343",
    "kind": "arxiv",
    "version": 2
  }
}