Pith Number

pith:QO2DPXZV

pith:2019:QO2DPXZVCUPLNJUGP2EY74KETZ

not attested not anchored not stored refs pending

A smooth shift approach for a Ramanujan expansion

Giovanni Coppola

arxiv:1901.01584 v3 · 2019-01-06 · 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{QO2DPXZVCUPLNJUGP2EY74KETZ}

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	2026-05-17T23:48:45.246696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83b437df35151eb6a6867e898ff1449e602a75740efe90e2ce3e0549155bd85b

Aliases

arxiv: 1901.01584 · arxiv_version: 1901.01584v3 · doi: 10.48550/arxiv.1901.01584 · pith_short_12: QO2DPXZVCUPL · pith_short_16: QO2DPXZVCUPLNJUG · pith_short_8: QO2DPXZV

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/QO2DPXZVCUPLNJUGP2EY74KETZ \
  | 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: 83b437df35151eb6a6867e898ff1449e602a75740efe90e2ce3e0549155bd85b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c70809b0db0b96a1f2cbfcb590c93ae1bdc803195790b9e61f0180de6410656",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-01-06T18:10:06Z",
    "title_canon_sha256": "5e237175bc0c9956ea14b6166633ddd165ec8e93ec6f8e6583741b3fd53f532b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.01584",
    "kind": "arxiv",
    "version": 3
  }
}