Pith Number

pith:B72XOJ4S

pith:2015:B72XOJ4S5NBUPBWGXKNXXVJB5J

not attested not anchored not stored refs pending

Linear Dependency of Translations and Square Integrable Representations

Ahmed Roman, Michael J. Puls, Peter A. Linnell

arxiv:1509.00493 v2 · 2015-09-01 · math.FA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B72XOJ4S5NBUPBWGXKNXXVJB5J}

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	2026-05-18T00:32:44.906042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ff5772792eb434786c6ba9b7bd521ea745a56a6f08f5de855b2192ec90c12fb

Aliases

arxiv: 1509.00493 · arxiv_version: 1509.00493v2 · doi: 10.48550/arxiv.1509.00493 · pith_short_12: B72XOJ4S5NBU · pith_short_16: B72XOJ4S5NBUPBWG · pith_short_8: B72XOJ4S

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/B72XOJ4S5NBUPBWGXKNXXVJB5J \
  | 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: 0ff5772792eb434786c6ba9b7bd521ea745a56a6f08f5de855b2192ec90c12fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e98e1badeb67fa6e1ac0cda1c34673b94edac456191a91f652073034c6a49e0f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-09-01T20:23:05Z",
    "title_canon_sha256": "42feba051ea9ebcd439fb9c73ee0cb03b20e3419b9f61b26f1efbb7f2985e653"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00493",
    "kind": "arxiv",
    "version": 2
  }
}