Pith Number

pith:HKG4XM2Z

pith:2014:HKG4XM2ZJSVBLWOXHDBKYWK77O

not attested not anchored not stored refs pending

New lower bounds on $\chi(R^d)$ for $d=8 \dots 12$

Birra Taha, Matthew Kahle

arxiv:1409.1278 v1 · 2014-09-03 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HKG4XM2ZJSVBLWOXHDBKYWK77O}

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	2026-05-18T02:43:27.389503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a8dcbb3594caa15d9d738c2ac595ffb8b28acb8aa7a91d75af9828346bd10cc

Aliases

arxiv: 1409.1278 · arxiv_version: 1409.1278v1 · doi: 10.48550/arxiv.1409.1278 · pith_short_12: HKG4XM2ZJSVB · pith_short_16: HKG4XM2ZJSVBLWOX · pith_short_8: HKG4XM2Z

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/HKG4XM2ZJSVBLWOXHDBKYWK77O \
  | 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: 3a8dcbb3594caa15d9d738c2ac595ffb8b28acb8aa7a91d75af9828346bd10cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e965adc8cadc25c11b26a495849fc4593335c6f4a1331b318d5d1383ed66ef4e",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-03T22:36:05Z",
    "title_canon_sha256": "21dab99e86eb49eeddeffa616caf682d9868ec869b406a56f5c163e194185977"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.1278",
    "kind": "arxiv",
    "version": 1
  }
}