Pith Number

pith:SDOY4JUB

pith:2025:SDOY4JUBJRFOWXTZHRVYL2WQJT

not attested not anchored not stored refs pending

Inner products on the Hilbert space $S_2$ of Hilbert--Schmidt operators

Josu\'e I. Rios-Cangas

arxiv:2506.04541 v1 · 2025-06-05 · math.FA · 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{SDOY4JUBJRFOWXTZHRVYL2WQJT}

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	2026-07-05T11:16:16.336448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90dd8e26814c4aeb5e793c6b85ead04cdd834446501327ebc1ac22381e56bab0

Aliases

arxiv: 2506.04541 · arxiv_version: 2506.04541v1 · doi: 10.48550/arxiv.2506.04541 · pith_short_12: SDOY4JUBJRFO · pith_short_16: SDOY4JUBJRFOWXTZ · pith_short_8: SDOY4JUB

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/SDOY4JUBJRFOWXTZHRVYL2WQJT \
  | 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: 90dd8e26814c4aeb5e793c6b85ead04cdd834446501327ebc1ac22381e56bab0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f145ce2e449ea589f6c3417c785ab12a8cba2fa99ff367379bce26d2d64a4ce7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-06-05T01:22:02Z",
    "title_canon_sha256": "5432801cb605e955fa86feb04c067f139f6db0d916907df9102c792440647056"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.04541",
    "kind": "arxiv",
    "version": 1
  }
}