Pith Number

pith:GM4GO2UJ

pith:2021:GM4GO2UJ4QKLR67YQBNR3KM66C

not attested not anchored not stored refs pending

A Multiplicative Property for Zero-Sums II

Chao Liu, David J. Grynkiewicz

arxiv:2109.10309 v1 · 2021-09-21 · math.NT · 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{GM4GO2UJ4QKLR67YQBNR3KM66C}

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	2026-07-05T03:16:27.830638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3338676a89e414b8fbf8805b1da99ef08b20c1fcfdce8225042dea26f84e9fb9

Aliases

arxiv: 2109.10309 · arxiv_version: 2109.10309v1 · doi: 10.48550/arxiv.2109.10309 · pith_short_12: GM4GO2UJ4QKL · pith_short_16: GM4GO2UJ4QKLR67Y · pith_short_8: GM4GO2UJ

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/GM4GO2UJ4QKLR67YQBNR3KM66C \
  | 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: 3338676a89e414b8fbf8805b1da99ef08b20c1fcfdce8225042dea26f84e9fb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d846cc5735b21eee93c06f55aeb8de4f6268639ac5e4bcf64b8de948c19ced9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-09-21T16:42:26Z",
    "title_canon_sha256": "e936598d589712b0139f65e65182803b3e74bb100ae589c54754bd7c838bdbec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.10309",
    "kind": "arxiv",
    "version": 1
  }
}