Pith Number

pith:DW6D3OIO

pith:2010:DW6D3OIOFQ3MLLWZMP4PCVZBWT

not attested not anchored not stored refs pending

On the size of identifying codes in triangle-free graphs

Adrian Kosowski (LaBRI, Andr\'e Raspaud (LaBRI), Florent Foucaud (LaBRI), INRIA Bordeaux - Sud-Ouest), Ralf Klasing (LaBRI

arxiv:1010.5975 v3 · 2010-10-28 · cs.DM · 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{DW6D3OIOFQ3MLLWZMP4PCVZBWT}

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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	2026-05-18T03:52:15.162109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1dbc3db90e2c36c5aed963f8f15721b4dca4cbb373e291f9174e3e1992dcb1b3

Aliases

arxiv: 1010.5975 · arxiv_version: 1010.5975v3 · doi: 10.48550/arxiv.1010.5975 · pith_short_12: DW6D3OIOFQ3M · pith_short_16: DW6D3OIOFQ3MLLWZ · pith_short_8: DW6D3OIO

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/DW6D3OIOFQ3MLLWZMP4PCVZBWT \
  | 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: 1dbc3db90e2c36c5aed963f8f15721b4dca4cbb373e291f9174e3e1992dcb1b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcb5c7b5ffb4a597984cb27d6fd3267c5cb005f4412cec3b2937471e34a123d7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2010-10-28T14:06:34Z",
    "title_canon_sha256": "998ff287feaa592dcc9c018ed1c3c2dd29cbee3a84f7989ac3769fc487f9b72f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.5975",
    "kind": "arxiv",
    "version": 3
  }
}