Pith Number

pith:S3RDLJ6M

pith:2012:S3RDLJ6MWPUGKF7FFNPVSAIBLI

not attested not anchored not stored refs pending

Self-adjoint, unitary, and normal weighted composition operators in several variables

Trieu Le

arxiv:1207.5980 v1 · 2012-07-25 · 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{S3RDLJ6MWPUGKF7FFNPVSAIBLI}

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	2026-05-18T03:50:09.744202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96e235a7ccb3e86517e52b5f5901015a23868e28a2ef9f4d0c87c990976373b4

Aliases

arxiv: 1207.5980 · arxiv_version: 1207.5980v1 · doi: 10.48550/arxiv.1207.5980 · pith_short_12: S3RDLJ6MWPUG · pith_short_16: S3RDLJ6MWPUGKF7F · pith_short_8: S3RDLJ6M

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/S3RDLJ6MWPUGKF7FFNPVSAIBLI \
  | 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: 96e235a7ccb3e86517e52b5f5901015a23868e28a2ef9f4d0c87c990976373b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abcc3c8a4d44a0c97301e3526bb17c699a66f2f082a99bb196afba6f5f0e0f2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-07-25T13:03:49Z",
    "title_canon_sha256": "b5155fd34d8758fe540ca7975b40390cf6a58ff5e0b3d2db79e64d95fd981ae0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5980",
    "kind": "arxiv",
    "version": 1
  }
}