Pith Number

pith:BBGI3QE5

pith:2018:BBGI3QE52X7CGFSVHQJYNFFWVG

not attested not anchored not stored refs pending

Functional Models and Invariant Subspaces for Pairs of Commuting Contractions

Haripada Sau, Joseph A. Ball

arxiv:1809.10248 v2 · 2018-09-26 · 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{BBGI3QE52X7CGFSVHQJYNFFWVG}

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	2026-05-18T00:04:35.326128Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

084c8dc09dd5fe2316553c138694b6a994950dd6574219bec20f344def1eb895

Aliases

arxiv: 1809.10248 · arxiv_version: 1809.10248v2 · doi: 10.48550/arxiv.1809.10248 · pith_short_12: BBGI3QE52X7C · pith_short_16: BBGI3QE52X7CGFSV · pith_short_8: BBGI3QE5

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/BBGI3QE52X7CGFSVHQJYNFFWVG \
  | 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: 084c8dc09dd5fe2316553c138694b6a994950dd6574219bec20f344def1eb895

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7485a9d4df87df384f42759a37adf052d3f9447c70f8abecb0634db686c13c1f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-09-26T21:58:06Z",
    "title_canon_sha256": "9e09c984224b9e741fd4da18169e6028e70396f1b0a1c15daa33497dcdff915c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.10248",
    "kind": "arxiv",
    "version": 2
  }
}