Pith Number

pith:F3QGKBCS

pith:2026:F3QGKBCS6TMOGFAPDKKY7WEZMA

not attested not anchored not stored refs pending

Spectra of generators of hyperbolic composition and weighted composition semigroups

Yong-Xin Gao, Ze-Hua Zhou

arxiv:2605.22048 v1 · 2026-05-21 · 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{F3QGKBCS6TMOGFAPDKKY7WEZMA}

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	2026-05-22T01:04:22.323270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ee0650452f4d8e3140f1a958fd899600a34f4019807390b7163462f2f0a831c

Aliases

arxiv: 2605.22048 · arxiv_version: 2605.22048v1 · doi: 10.48550/arxiv.2605.22048 · pith_short_12: F3QGKBCS6TMO · pith_short_16: F3QGKBCS6TMOGFAP · pith_short_8: F3QGKBCS

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/F3QGKBCS6TMOGFAPDKKY7WEZMA \
  | 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: 2ee0650452f4d8e3140f1a958fd899600a34f4019807390b7163462f2f0a831c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3db5239496f30dbd0faf487f1552e904b98de23bdebe9d5920fdba2e3bad6f22",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-21T06:34:54Z",
    "title_canon_sha256": "0b3ff2ad12776ff31b5561808545e6e954c3f7a94dfbf0944a755160545803c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22048",
    "kind": "arxiv",
    "version": 1
  }
}