Pith Number

pith:TF4EJ3G7

pith:2017:TF4EJ3G72ICRFJUXK5YSW4OYDY

not attested not anchored not stored refs pending

Arithmetic properties of coefficients of power series expansion of $\prod_{n=0}^{\infty}\left(1-x^{2^{n}}\right)^{t}$ (with an Appendix by Andrzej Schinzel)

Maciej Gawron, Maciej Ulas, Piotr Miska

arxiv:1703.01955 v1 · 2017-03-06 · 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{TF4EJ3G72ICRFJUXK5YSW4OYDY}

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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	2026-05-18T00:49:29.172363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

997844ecdfd20512a69757712b71d81e0488a76659589f32cd5053196bd19828

Aliases

arxiv: 1703.01955 · arxiv_version: 1703.01955v1 · doi: 10.48550/arxiv.1703.01955 · pith_short_12: TF4EJ3G72ICR · pith_short_16: TF4EJ3G72ICRFJUX · pith_short_8: TF4EJ3G7

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/TF4EJ3G72ICRFJUXK5YSW4OYDY \
  | 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: 997844ecdfd20512a69757712b71d81e0488a76659589f32cd5053196bd19828

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d72e0b2d48b505d86fea1836789efe6ab60761721d7698fd44ef32412f42f4c9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-03-06T16:28:31Z",
    "title_canon_sha256": "ac76b0d9bcf8c5c5cdd3dddb143ff5dc2cb2c6a962a7936286653a2e0c604f1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.01955",
    "kind": "arxiv",
    "version": 1
  }
}