Pith Number

pith:VMNHOCEM

pith:2021:VMNHOCEMLJZ6SQUESOXWG342ZH

not attested not anchored not stored refs pending

Metric dimension on sparse graphs and its applications to zero forcing sets

Aline Parreau, Ignacio M. Pelayo, Nicolas Bousquet, Quentin Deschamps

arxiv:2111.07845 v2 · 2021-11-15 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMNHOCEMLJZ6SQUESOXWG342ZH}

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	2026-07-05T04:28:28.847307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab1a77088c5a73e9428493af636f9ac9e3c81f9742d6ed45423ca352bf254b6c

Aliases

arxiv: 2111.07845 · arxiv_version: 2111.07845v2 · doi: 10.48550/arxiv.2111.07845 · pith_short_12: VMNHOCEMLJZ6 · pith_short_16: VMNHOCEMLJZ6SQUE · pith_short_8: VMNHOCEM

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/VMNHOCEMLJZ6SQUESOXWG342ZH \
  | 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: ab1a77088c5a73e9428493af636f9ac9e3c81f9742d6ed45423ca352bf254b6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87de3d08c255330d0e71695bfcebc2e3420702622719fbca43e305496d1ccd23",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-11-15T15:33:03Z",
    "title_canon_sha256": "be194e1c3cd5f0aad6b43a37d1a985652f1b87912aa0635a85d2cd2596505cb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.07845",
    "kind": "arxiv",
    "version": 2
  }
}