Pith Number

pith:J2O6IPPV

pith:2015:J2O6IPPVE6FDC4OLJHFCZQVV34

not attested not anchored not stored refs pending

Completeness of Gabor systems

Antti Haimi, Jos\'e Luis Romero, Karlheinz Gr\"ochenig

arxiv:1507.02124 v3 · 2015-07-08 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J2O6IPPVE6FDC4OLJHFCZQVV34}

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	2026-05-18T00:56:31.707327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e9de43df5278a3171cb49ca2cc2b5df24108bb9feb563ae772c8909f62aa944

Aliases

arxiv: 1507.02124 · arxiv_version: 1507.02124v3 · doi: 10.48550/arxiv.1507.02124 · pith_short_12: J2O6IPPVE6FD · pith_short_16: J2O6IPPVE6FDC4OL · pith_short_8: J2O6IPPV

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/J2O6IPPVE6FDC4OLJHFCZQVV34 \
  | 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: 4e9de43df5278a3171cb49ca2cc2b5df24108bb9feb563ae772c8909f62aa944

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de87186ed53f3429f22a9c038f396d9ff46f4a7972cfb871cb5f3b2ad994b826",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-07-08T12:37:12Z",
    "title_canon_sha256": "421326e0ef508949ab5abffd29e7881b195acac89898d363160e5467ca6a2d63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02124",
    "kind": "arxiv",
    "version": 3
  }
}