Pith Number

pith:WZCPWOSJ

pith:2024:WZCPWOSJMVFDYWD2INZYNT6TQG

not attested not anchored not stored refs pending

Popa's "Recurrent Sequences" and Reciprocity

Steven Finch

arxiv:2412.11806 v3 · 2024-12-16 · math.CA · cs.DM · math.CO · 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{WZCPWOSJMVFDYWD2INZYNT6TQG}

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.

Cited by

1 paper in Pith

Exercises in Iterational Asymptotics

Receipt and verification

First computed	2026-07-05T11:25:06.434034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b644fb3a49654a3c587a437386cfd381ad33221c22ee07e9e415502d36eda096

Aliases

arxiv: 2412.11806 · arxiv_version: 2412.11806v3 · doi: 10.48550/arxiv.2412.11806 · pith_short_12: WZCPWOSJMVFD · pith_short_16: WZCPWOSJMVFDYWD2 · pith_short_8: WZCPWOSJ

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/WZCPWOSJMVFDYWD2INZYNT6TQG \
  | 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: b644fb3a49654a3c587a437386cfd381ad33221c22ee07e9e415502d36eda096

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1ef30872fb0566e0f0b6175f5ea00a136e9cca85a2b4ad879bf0217e6650f05",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2024-12-16T14:17:46Z",
    "title_canon_sha256": "d4c5f9cb4e83ca20b2ce923978840b744d2222de1fcfb80119228a2bd2033405"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11806",
    "kind": "arxiv",
    "version": 3
  }
}