Pith Number

pith:QRM6FFNX

pith:2013:QRM6FFNXLJXWKCW4DFYXF2ZOPC

not attested not anchored not stored refs pending

Spectral bounds for the independence ratio and the chromatic number of an operator

Christine Bachoc, Evan DeCorte, Fernando Mario de Oliveira Filho, Frank Vallentin

arxiv:1301.1054 v2 · 2013-01-06 · math.FA · math.CO · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QRM6FFNXLJXWKCW4DFYXF2ZOPC}

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	2026-05-18T02:41:09.162291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8459e295b75a6f650adc197172eb2e7894289ec7a50565de94d75942a4d7a414

Aliases

arxiv: 1301.1054 · arxiv_version: 1301.1054v2 · doi: 10.48550/arxiv.1301.1054 · pith_short_12: QRM6FFNXLJXW · pith_short_16: QRM6FFNXLJXWKCW4 · pith_short_8: QRM6FFNX

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/QRM6FFNXLJXWKCW4DFYXF2ZOPC \
  | 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: 8459e295b75a6f650adc197172eb2e7894289ec7a50565de94d75942a4d7a414

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9241920a989079d09317c2389c2eb005bb29df00da2f6e8ac0d45e4ef7ebdb1f",
    "cross_cats_sorted": [
      "math.CO",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-01-06T20:58:33Z",
    "title_canon_sha256": "11b0dcb57304cc632f87245d7502b60eb83410aa47c047ab2a37adf2e1fde8e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1054",
    "kind": "arxiv",
    "version": 2
  }
}