Pith Number

pith:F4W4SB3P

pith:2025:F4W4SB3PGIL7XOTHUSEBCE2X32

not attested not anchored not stored refs pending

Good Ramanujan Expansions: A suitably enhanced decay of coefficients has important consequences

Giovanni Coppola

arxiv:2509.24456 v2 · 2025-09-29 · 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{F4W4SB3PGIL7XOTHUSEBCE2X32}

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	2026-06-02T02:04:09.275964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f2dc9076f3217fbba67a488111357deaec28f20f0afb1ae1f296019b61d4663

Aliases

arxiv: 2509.24456 · arxiv_version: 2509.24456v2 · doi: 10.48550/arxiv.2509.24456 · pith_short_12: F4W4SB3PGIL7 · pith_short_16: F4W4SB3PGIL7XOTH · pith_short_8: F4W4SB3P

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/F4W4SB3PGIL7XOTHUSEBCE2X32 \
  | 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: 2f2dc9076f3217fbba67a488111357deaec28f20f0afb1ae1f296019b61d4663

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "211648dc37abcbe8354d77d7579d443947519784217d3ff07864c1e9d3995401",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-09-29T08:37:59Z",
    "title_canon_sha256": "3663c9d8f05c7a98d8adcaaef8009ba0457ef8d2f19c93ee74e127255bc54dba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.24456",
    "kind": "arxiv",
    "version": 2
  }
}