Pith Number

pith:XRDE4YAZ

pith:2012:XRDE4YAZXC4O22XLIQ2SJA5N5N

not attested not anchored not stored refs pending

Sobolev spaces on locally compact abelian groups

Enrique G. Reyes, Przemys{\l}aw G\'orka

arxiv:1208.3053 v1 · 2012-08-15 · math-ph · hep-th · 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{XRDE4YAZXC4O22XLIQ2SJA5N5N}

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	2026-05-18T03:48:45.735048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc464e6019b8b8ed6aeb44352483adeb7b7f4251bebc88a84a095b6ef62422ec

Aliases

arxiv: 1208.3053 · arxiv_version: 1208.3053v1 · doi: 10.48550/arxiv.1208.3053 · pith_short_12: XRDE4YAZXC4O · pith_short_16: XRDE4YAZXC4O22XL · pith_short_8: XRDE4YAZ

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/XRDE4YAZXC4O22XLIQ2SJA5N5N \
  | 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: bc464e6019b8b8ed6aeb44352483adeb7b7f4251bebc88a84a095b6ef62422ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ad84edd582612a3cc88148f12eab7bd6600aa95f33c7517d241fe73c9f5f878",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-08-15T08:19:24Z",
    "title_canon_sha256": "29fed1891674b173752885ea60f5a700df878b40c179465afdfa1335f7df1391"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3053",
    "kind": "arxiv",
    "version": 1
  }
}