Pith Number

pith:HCPMFILX

pith:2013:HCPMFILXETAIYEPK2PJSFHI4UU

not attested not anchored not stored refs pending

Inner product spaces and Krein spaces in the quaternionic setting

Daniel Alpay, Fabrizio Colombo, Irene Sabadini

arxiv:1303.1076 v2 · 2013-03-05 · 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{HCPMFILXETAIYEPK2PJSFHI4UU}

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	2026-05-18T03:15:43.383844Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

389ec2a17724c08c11ead3d3229d1ca5079398ed37a848e318578bc1cc1967ed

Aliases

arxiv: 1303.1076 · arxiv_version: 1303.1076v2 · doi: 10.48550/arxiv.1303.1076 · pith_short_12: HCPMFILXETAI · pith_short_16: HCPMFILXETAIYEPK · pith_short_8: HCPMFILX

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/HCPMFILXETAIYEPK2PJSFHI4UU \
  | 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: 389ec2a17724c08c11ead3d3229d1ca5079398ed37a848e318578bc1cc1967ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6074732838f54ac582592b88143d97f7495552eda347302a18c27ca5987ddef5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-03-05T15:48:57Z",
    "title_canon_sha256": "d5549b652c37a728df41b45501dd3f21fcbb93c7dceb92c2fe9701956a429ea4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1076",
    "kind": "arxiv",
    "version": 2
  }
}