Pith Number

pith:I7FPLKSD

pith:2015:I7FPLKSDUX3QFX4VLROJURFUUA

not attested not anchored not stored refs pending

Spectra of weighted composition operators induced by automorphisms

Yong-Xin Gao, Ze-Hua Zhou

arxiv:1507.05773 v6 · 2015-07-21 · 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{I7FPLKSDUX3QFX4VLROJURFUUA}

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	2026-05-18T00:40:24.503018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47caf5aa43a5f702df955c5c9a44b4a02a5a8642a9e264efa2310ec5a223af2f

Aliases

arxiv: 1507.05773 · arxiv_version: 1507.05773v6 · doi: 10.48550/arxiv.1507.05773 · pith_short_12: I7FPLKSDUX3Q · pith_short_16: I7FPLKSDUX3QFX4V · pith_short_8: I7FPLKSD

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/I7FPLKSDUX3QFX4VLROJURFUUA \
  | 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: 47caf5aa43a5f702df955c5c9a44b4a02a5a8642a9e264efa2310ec5a223af2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d37ca2d55f65cd40c848fd16eb123592bc0efc145f761b0b32df2e5aefd53af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-07-21T10:24:05Z",
    "title_canon_sha256": "ef92f6354a29b243b5c220f15447e11507bfb3ee170ffabde04870713291a307"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05773",
    "kind": "arxiv",
    "version": 6
  }
}