Pith Number

pith:5KJ7DKV2

pith:2012:5KJ7DKV2GWAAEUFFJYPDSA654V

not attested not anchored not stored refs pending

Extensions of Fractional Precolorings show Discontinuous Behavior

Daniel Kral, Jan van den Heuvel, Jan Volec, Jean-Sebastien Sereni, Martin Kupec

arxiv:1205.5405 v2 · 2012-05-24 · 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{5KJ7DKV2GWAAEUFFJYPDSA654V}

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	2026-05-18T03:04:24.358292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea93f1aaba35800250a54e1e3903dde57db36afb5fb6d72ec1db919448d20413

Aliases

arxiv: 1205.5405 · arxiv_version: 1205.5405v2 · doi: 10.48550/arxiv.1205.5405 · pith_short_12: 5KJ7DKV2GWAA · pith_short_16: 5KJ7DKV2GWAAEUFF · pith_short_8: 5KJ7DKV2

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/5KJ7DKV2GWAAEUFFJYPDSA654V \
  | 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: ea93f1aaba35800250a54e1e3903dde57db36afb5fb6d72ec1db919448d20413

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ef6b382c8a4f8bf9c20f6662c86763002dbabbe585bc77a0bba32b608c2220a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-24T11:42:45Z",
    "title_canon_sha256": "ee59483050c9eeaecf968d968498dc5caf50f4e90bb530f730299c10f40ea8c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5405",
    "kind": "arxiv",
    "version": 2
  }
}