Pith Number

pith:FHPYJQEB

pith:2021:FHPYJQEBSHRMWBN2ANVS7KZMTU

not attested not anchored not stored refs pending

Asymptotics for the twisted eta-product and applications to sign changes in partitions

Johann Franke, Taylor Garnowski, Walter Bridges

arxiv:2111.04183 v4 · 2021-11-07 · 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{FHPYJQEBSHRMWBN2ANVS7KZMTU}

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	2026-07-05T04:52:15.370353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29df84c08191e2cb05ba036b2fab2c9d340b1e3c696691e21d22c0be936141e0

Aliases

arxiv: 2111.04183 · arxiv_version: 2111.04183v4 · doi: 10.48550/arxiv.2111.04183 · pith_short_12: FHPYJQEBSHRM · pith_short_16: FHPYJQEBSHRMWBN2 · pith_short_8: FHPYJQEB

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/FHPYJQEBSHRMWBN2ANVS7KZMTU \
  | 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: 29df84c08191e2cb05ba036b2fab2c9d340b1e3c696691e21d22c0be936141e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75dde8bb1196648f1207587eaf38790d3a84964e142e6bc27305a79d608d08a0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-11-07T21:36:24Z",
    "title_canon_sha256": "6f1f6ee3df6287ca6ea16beaa1a0290602adb91f0f7a8c23359ec6ed2fb78335"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.04183",
    "kind": "arxiv",
    "version": 4
  }
}