Pith Number

pith:T4UXXQS5

pith:2013:T4UXXQS53JYKETY2XKT5RSDSM5

not attested not anchored not stored refs pending

$\Gamma$-unitaries, dilation and a natural example

Haripada Sau, Tirthankar Bhattacharyya

arxiv:1311.1577 v4 · 2013-11-07 · 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{T4UXXQS53JYKETY2XKT5RSDSM5}

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	2026-05-18T01:19:16.333786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f297bc25dda70a24f1abaa7d8c872674e1c6fad39169e8e085a353b5bf165d9

Aliases

arxiv: 1311.1577 · arxiv_version: 1311.1577v4 · doi: 10.48550/arxiv.1311.1577 · pith_short_12: T4UXXQS53JYK · pith_short_16: T4UXXQS53JYKETY2 · pith_short_8: T4UXXQS5

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/T4UXXQS53JYKETY2XKT5RSDSM5 \
  | 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: 9f297bc25dda70a24f1abaa7d8c872674e1c6fad39169e8e085a353b5bf165d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f0f4853c5f4b3fd6f41e29a504f1ee3bdf0629f74995a9da49ca110ef395826",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-07T05:06:26Z",
    "title_canon_sha256": "136d70415e7f16fa6e923105571171954e278980e3a9c2b44f2867d77fbc9f91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1577",
    "kind": "arxiv",
    "version": 4
  }
}