Pith Number

pith:CMKS3R6X

pith:2015:CMKS3R6XG2B4OOV66DS2YMVJQS

not attested not anchored not stored refs pending

Sparse sum-of-squares certificates on finite abelian groups

Hamza Fawzi, James Saunderson, Pablo A. Parrilo

arxiv:1503.01207 v1 · 2015-03-04 · math.OC · 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{CMKS3R6XG2B4OOV66DS2YMVJQS}

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	2026-05-18T00:56:26.188399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13152dc7d73683c73abef0e5ac32a984a7abaf5e5945ec28e430516306198ff1

Aliases

arxiv: 1503.01207 · arxiv_version: 1503.01207v1 · doi: 10.48550/arxiv.1503.01207 · pith_short_12: CMKS3R6XG2B4 · pith_short_16: CMKS3R6XG2B4OOV6 · pith_short_8: CMKS3R6X

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/CMKS3R6XG2B4OOV66DS2YMVJQS \
  | 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: 13152dc7d73683c73abef0e5ac32a984a7abaf5e5945ec28e430516306198ff1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6202a5346278c1623c08562a78b3e1903c6aeca90df6ef8a92a495f862cf05da",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-03-04T03:54:21Z",
    "title_canon_sha256": "f5b24fe05764c4fd010ec4eab68cc22db88772419ccf220792dcb5f41c656db5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.01207",
    "kind": "arxiv",
    "version": 1
  }
}