Pith Number

pith:V2FYWAYV

pith:2012:V2FYWAYVNC4Z5XFI22OWKRDVLY

not attested not anchored not stored refs pending

Construction of concrete orthonormal basis for (L^2,\Gamma,\chi)-theta functions associated to discrete subgroups of rank one in (C,+)

Ahmed Intissar, Allal Ghanmi

arxiv:1212.1870 v1 · 2012-12-09 · math.CV · math-ph · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V2FYWAYVNC4Z5XFI22OWKRDVLY}

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	2026-05-18T01:52:46.157497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae8b8b031568b99edca8d69d6544755e02d505ebed73c38cd4fdff70c06d7dd6

Aliases

arxiv: 1212.1870 · arxiv_version: 1212.1870v1 · doi: 10.48550/arxiv.1212.1870 · pith_short_12: V2FYWAYVNC4Z · pith_short_16: V2FYWAYVNC4Z5XFI · pith_short_8: V2FYWAYV

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/V2FYWAYVNC4Z5XFI22OWKRDVLY \
  | 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: ae8b8b031568b99edca8d69d6544755e02d505ebed73c38cd4fdff70c06d7dd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b20e6a634f28ba694d3147077d817615dd2d46c8ba979cb35ca5a2d58916c939",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2012-12-09T09:41:49Z",
    "title_canon_sha256": "0beb3c36f2275674595d58ffd52c4263a65fd864290b5411a6e462e719ffeb8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1870",
    "kind": "arxiv",
    "version": 1
  }
}