Pith Number

pith:UB225QU5

pith:2025:UB225QU5NL2VJF5JIWOOKRHXKW

not attested not anchored not stored refs pending

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions

A. Vanitha, M. P. Chaudhary, Nasser Abdo Saeed Bulkhali

arxiv:2507.13645 v1 · 2025-07-18 · 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{UB225QU5NL2VJF5JIWOOKRHXKW}

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	2026-07-05T11:39:20.613294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a075aec29d6af55497a9459ce544f7559f701c732e52e546f3e56db46cf63ce6

Aliases

arxiv: 2507.13645 · arxiv_version: 2507.13645v1 · doi: 10.48550/arxiv.2507.13645 · pith_short_12: UB225QU5NL2V · pith_short_16: UB225QU5NL2VJF5J · pith_short_8: UB225QU5

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/UB225QU5NL2VJF5JIWOOKRHXKW \
  | 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: a075aec29d6af55497a9459ce544f7559f701c732e52e546f3e56db46cf63ce6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a04cf362b3ade1460d0966067717dcb4d987178d4a4b200305f0aef0a2194418",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-18T04:15:40Z",
    "title_canon_sha256": "ba96dcaa4f1c2ada52641423394be7226700dab9ed9f6cc1a112a971c50f03df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13645",
    "kind": "arxiv",
    "version": 1
  }
}