Pith Number

pith:FH65YH4H

pith:2021:FH65YH4H7SIATBJQY7767MLY2N

not attested not anchored not stored refs pending

A Multiplicative Property for Zero-Sums I

Chao Liu, David J. Grynkiewicz

arxiv:2109.10300 v1 · 2021-09-21 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FH65YH4H7SIATBJQY7767MLY2N}

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	2026-07-05T03:16:27.696399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29fddc1f87fc90098530c7ffefb178d3473fc9b0601affe5419bf203e07a788e

Aliases

arxiv: 2109.10300 · arxiv_version: 2109.10300v1 · doi: 10.48550/arxiv.2109.10300 · pith_short_12: FH65YH4H7SIA · pith_short_16: FH65YH4H7SIATBJQ · pith_short_8: FH65YH4H

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/FH65YH4H7SIATBJQY7767MLY2N \
  | 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: 29fddc1f87fc90098530c7ffefb178d3473fc9b0601affe5419bf203e07a788e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26a3436a006b81a0cbb759ff7d5cd4f2a2358f1c7a3ac676d349c92867700635",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-09-21T16:23:31Z",
    "title_canon_sha256": "d0079d0e5bf33165fa2bacd3671a098e35c9a6c3390994fd92d39c406eed1efb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.10300",
    "kind": "arxiv",
    "version": 1
  }
}