Pith Number

pith:VHPDNEQU

pith:2007:VHPDNEQUZIFCRPXAZRO7IGWZCH

not attested not anchored not stored refs pending

Unitary processes with independent increments and representations of Hilbert tensor algebras

Kalyan B. Sinha, Lingaraj Sahu, Michael Sch\"urmann

arxiv:0712.1896 v2 · 2007-12-12 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VHPDNEQUZIFCRPXAZRO7IGWZCH}

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	2026-05-18T04:09:04.308622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9de369214ca0a28bee0cc5df41ad911ee27f3f76e1b20506be3203ece0483dd

Aliases

arxiv: 0712.1896 · arxiv_version: 0712.1896v2 · doi: 10.48550/arxiv.0712.1896 · pith_short_12: VHPDNEQUZIFC · pith_short_16: VHPDNEQUZIFCRPXA · pith_short_8: VHPDNEQU

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/VHPDNEQUZIFCRPXAZRO7IGWZCH \
  | 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: a9de369214ca0a28bee0cc5df41ad911ee27f3f76e1b20506be3203ece0483dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c278e53b70f2d521e3a1efce02c72dd5b00c92522f0747a11cffba9f5dad6ae",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2007-12-12T10:19:58Z",
    "title_canon_sha256": "9b1e74f1e193ce887cb9591a1d1e9c1f0836c60df6d9c58d46953e94df65ee7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.1896",
    "kind": "arxiv",
    "version": 2
  }
}