Pith Number

pith:VEMR3D62

pith:2015:VEMR3D62HEEDDAKAOCFFPLKZ7T

not attested not anchored not stored refs pending

Explaining Ramanujan's "Unclosed" Comment in His Last Letter to Hardy

Daniel Parry

arxiv:1512.07436 v3 · 2015-12-23 · 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{VEMR3D62HEEDDAKAOCFFPLKZ7T}

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	2026-05-18T01:23:32.052808Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9191d8fda3908318140708a57ad59fce9dfa227a2ae372239354ed8ef5ebcc2

Aliases

arxiv: 1512.07436 · arxiv_version: 1512.07436v3 · doi: 10.48550/arxiv.1512.07436 · pith_short_12: VEMR3D62HEED · pith_short_16: VEMR3D62HEEDDAKA · pith_short_8: VEMR3D62

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/VEMR3D62HEEDDAKAOCFFPLKZ7T \
  | 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: a9191d8fda3908318140708a57ad59fce9dfa227a2ae372239354ed8ef5ebcc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98491fc8a441deb1d6f972ee2a7c83f9eca07fe0f3707155fa060c11544aa091",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-23T11:23:28Z",
    "title_canon_sha256": "17f531dd597ac76537a96ebfb785784ab6870bf8d54a56614503b2db61618bda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07436",
    "kind": "arxiv",
    "version": 3
  }
}