Pith Number

pith:MB3H4UOZ

pith:2020:MB3H4UOZYMW6TQSDVFEGEINMF3

not attested not anchored not stored refs pending

Equivalence of classical and quantum completeness for real principal type operators on the circle

Kouichi Taira

arxiv:2004.07547 v4 · 2020-04-16 · math.AP · math-ph · math.MP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MB3H4UOZYMW6TQSDVFEGEINMF3}

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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.

Cited by

1 paper in Pith

Dirac operators and local invariants on perturbations of Minkowski space

Receipt and verification

First computed	2026-07-05T08:50:05.064093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60767e51d9c32de9c243a9486221ac2ed4e08e57c94a5cbc1888624a9d190a7c

Aliases

arxiv: 2004.07547 · arxiv_version: 2004.07547v4 · doi: 10.48550/arxiv.2004.07547 · pith_short_12: MB3H4UOZYMW6 · pith_short_16: MB3H4UOZYMW6TQSD · pith_short_8: MB3H4UOZ

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/MB3H4UOZYMW6TQSDVFEGEINMF3 \
  | 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: 60767e51d9c32de9c243a9486221ac2ed4e08e57c94a5cbc1888624a9d190a7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebdde918045bed1a7741fab3efae02b40290f8b0862ec88a44f28a43b575a9be",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-04-16T09:30:41Z",
    "title_canon_sha256": "5c8746b56fe9867a2983f2708de3bad0bf495d6ed4372fdbfb4c9b11218af87f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.07547",
    "kind": "arxiv",
    "version": 4
  }
}