Pith Number

pith:RNHIWOBH

pith:2012:RNHIWOBHWFJJNNZEYM2GZM6FAT

not attested not anchored not stored refs pending

Unified spectral bounds on the chromatic number

Clive Elphick, Pawel Wocjan

arxiv:1210.7844 v5 · 2012-10-29 · math.CO · cs.DM · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RNHIWOBHWFJJNNZEYM2GZM6FAT}

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	2026-05-18T02:39:09.301305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b4e8b3827b15296b724c3346cb3c504d8b76435a124226fe9e335f7e14e370f

Aliases

arxiv: 1210.7844 · arxiv_version: 1210.7844v5 · doi: 10.48550/arxiv.1210.7844 · pith_short_12: RNHIWOBHWFJJ · pith_short_16: RNHIWOBHWFJJNNZE · pith_short_8: RNHIWOBH

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/RNHIWOBHWFJJNNZEYM2GZM6FAT \
  | 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: 8b4e8b3827b15296b724c3346cb3c504d8b76435a124226fe9e335f7e14e370f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef990c29386f91ebe3e1636f2cf83653a43a77cddff24436afb16963dd76e851",
    "cross_cats_sorted": [
      "cs.DM",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-29T21:17:01Z",
    "title_canon_sha256": "50cd4f5ddb9ba2449bec7c616956c7d6690f6ea5a00f171677b44c67387c1c46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7844",
    "kind": "arxiv",
    "version": 5
  }
}