Pith Number

pith:O3VXNYT6

pith:2016:O3VXNYT6RTFQZYCCLLWSRWXIXL

not attested not anchored not stored refs pending

Complex symmetric composition operators induced by linear fractional transformations

Yong-Xin Gao, Ze-Hua Zhou

arxiv:1608.01288 v3 · 2016-08-03 · 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{O3VXNYT6RTFQZYCCLLWSRWXIXL}

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	2026-05-18T00:51:57.682784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76eb76e27e8ccb0ce0425aed28dae8bafcb463cb67ef41d926fcb737b65a0d47

Aliases

arxiv: 1608.01288 · arxiv_version: 1608.01288v3 · doi: 10.48550/arxiv.1608.01288 · pith_short_12: O3VXNYT6RTFQ · pith_short_16: O3VXNYT6RTFQZYCC · pith_short_8: O3VXNYT6

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/O3VXNYT6RTFQZYCCLLWSRWXIXL \
  | 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: 76eb76e27e8ccb0ce0425aed28dae8bafcb463cb67ef41d926fcb737b65a0d47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc1dd055d876769866ec6d7098087dcc44981d044798757c60893123425d9bc2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-08-03T19:03:41Z",
    "title_canon_sha256": "b7b24d722fdf139eeb09b2bb91a86b963ea3b496335a14e0fa1efe7f757f582e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.01288",
    "kind": "arxiv",
    "version": 3
  }
}