Pith Number

pith:SAJ5GCC5

pith:2018:SAJ5GCC5JRCHYU3A5T57NTTGGJ

not attested not anchored not stored refs pending

The Closed Extensions of a Closed Operator

Christoph Fischbacher

arxiv:1807.03471 v2 · 2018-07-10 · 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{SAJ5GCC5JRCHYU3A5T57NTTGGJ}

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	2026-05-18T00:03:36.710671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9013d3085d4c447c5360ecfbf6ce66325651ddb7143762686438a9a63dad54ed

Aliases

arxiv: 1807.03471 · arxiv_version: 1807.03471v2 · doi: 10.48550/arxiv.1807.03471 · pith_short_12: SAJ5GCC5JRCH · pith_short_16: SAJ5GCC5JRCHYU3A · pith_short_8: SAJ5GCC5

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/SAJ5GCC5JRCHYU3A5T57NTTGGJ \
  | 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: 9013d3085d4c447c5360ecfbf6ce66325651ddb7143762686438a9a63dad54ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78e5e61cefaa3624b185db986492e34f5ae127ad34a7b9ebff33ba01d528045b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-07-10T03:41:16Z",
    "title_canon_sha256": "8453189793d7971a67b99d1a4c883cb03cdd49b0b941e9a320dea3e75e04723b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.03471",
    "kind": "arxiv",
    "version": 2
  }
}