Pith Number

pith:7VH6SI74

pith:2016:7VH6SI74JFBMVR3ORBSYIPEH6H

not attested not anchored not stored refs pending

Short proofs for $q$-Raabe formula and integrals for Jacobi theta functions

Mohamed El Bachraoui

arxiv:1609.06895 v1 · 2016-09-22 · 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{7VH6SI74JFBMVR3ORBSYIPEH6H}

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	2026-05-18T01:04:04.868578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd4fe923fc4942cac76e8865843c87f1f8ad85d16e9d956120e2bb6c61781b1a

Aliases

arxiv: 1609.06895 · arxiv_version: 1609.06895v1 · doi: 10.48550/arxiv.1609.06895 · pith_short_12: 7VH6SI74JFBM · pith_short_16: 7VH6SI74JFBMVR3O · pith_short_8: 7VH6SI74

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/7VH6SI74JFBMVR3ORBSYIPEH6H \
  | 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: fd4fe923fc4942cac76e8865843c87f1f8ad85d16e9d956120e2bb6c61781b1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a089fc1ab2e430992712382193a15575929b97b70584c629485ada3226d9919",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-22T10:13:06Z",
    "title_canon_sha256": "c633020e00ec5b0a58d09345b3e44d0e0cfca0b15d795aa78e4e3817baaa94d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06895",
    "kind": "arxiv",
    "version": 1
  }
}