Pith Number

pith:C3X3BGJD

pith:2015:C3X3BGJDQCZUU76ZDQWE6G4CC2

not attested not anchored not stored refs pending

Low Degree Nullstellensatz Certificates for 3-Colorability

Benjamin Lowenstein, Bo Li, Mohamed Omar

arxiv:1503.04680 v1 · 2015-03-16 · 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{C3X3BGJDQCZUU76ZDQWE6G4CC2}

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	2026-05-18T02:23:24.295088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16efb0992380b34a7fd91c2c4f1b8216944494bbddf1ef3490d9b2ea543085fd

Aliases

arxiv: 1503.04680 · arxiv_version: 1503.04680v1 · doi: 10.48550/arxiv.1503.04680 · pith_short_12: C3X3BGJDQCZU · pith_short_16: C3X3BGJDQCZUU76Z · pith_short_8: C3X3BGJD

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/C3X3BGJDQCZUU76ZDQWE6G4CC2 \
  | 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: 16efb0992380b34a7fd91c2c4f1b8216944494bbddf1ef3490d9b2ea543085fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55aa48e7a9b4e4337bca28a915a6e91e5dd6d8d38c9d80f310a7295f7b8c0477",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-03-16T15:15:49Z",
    "title_canon_sha256": "8de9203fbaeda9d174021cb4dcd7e3855e7e7c9ca524ac284df2f97e8eb88db9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04680",
    "kind": "arxiv",
    "version": 1
  }
}