Pith Number

pith:FU7GUBFJ

pith:2018:FU7GUBFJUCZMWAEX2B266EYH5I

not attested not anchored not stored refs pending

Sum-Product Phenomena for Planar Hypercomplex Numbers

Adam Sheffer, Matthew Hase-Liu

arxiv:1812.09547 v1 · 2018-12-22 · 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{FU7GUBFJUCZMWAEX2B266EYH5I}

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	2026-05-17T23:57:27.583882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d3e6a04a9a0b2cb0097d075ef1307ea177abb0d3f4073c429630331f5366259

Aliases

arxiv: 1812.09547 · arxiv_version: 1812.09547v1 · doi: 10.48550/arxiv.1812.09547 · pith_short_12: FU7GUBFJUCZM · pith_short_16: FU7GUBFJUCZMWAEX · pith_short_8: FU7GUBFJ

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/FU7GUBFJUCZMWAEX2B266EYH5I \
  | 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: 2d3e6a04a9a0b2cb0097d075ef1307ea177abb0d3f4073c429630331f5366259

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94cdef86056dbd91986f6f8ed6d870e13b6887082f261349ac8e2b465b7df734",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-12-22T15:45:15Z",
    "title_canon_sha256": "293ec5d4ffa3f68c16701dcaebd1bd260764b4569881da53555b2aff948c8c46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09547",
    "kind": "arxiv",
    "version": 1
  }
}