Pith Number

pith:3TM3BEGR

pith:2016:3TM3BEGR7TVAGQBZCXL6ARZB3P

not attested not anchored not stored refs pending

Arithmetic properties for cubic partition pairs modulo powers of 3

Shane Chern

arxiv:1609.08578 v1 · 2016-09-27 · 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{3TM3BEGR7TVAGQBZCXL6ARZB3P}

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	2026-05-18T00:31:51.881763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcd9b090d1fcea03403915d7e04721dbffecad5cfbad7bcfb24fdf2fa9214fa9

Aliases

arxiv: 1609.08578 · arxiv_version: 1609.08578v1 · doi: 10.48550/arxiv.1609.08578 · pith_short_12: 3TM3BEGR7TVA · pith_short_16: 3TM3BEGR7TVAGQBZ · pith_short_8: 3TM3BEGR

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/3TM3BEGR7TVAGQBZCXL6ARZB3P \
  | 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: dcd9b090d1fcea03403915d7e04721dbffecad5cfbad7bcfb24fdf2fa9214fa9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80e1a8d3cfd2005fa4c884dac82bcc029d4b5d30dcd7e489b2e8f0d51e791570",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-27T18:55:44Z",
    "title_canon_sha256": "1eee014729d165faf9a0fdf5e9cc06ce4073fd8f48289f1f1832cbe3a9633c0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.08578",
    "kind": "arxiv",
    "version": 1
  }
}