Pith Number

pith:53YCK2Q5

pith:2016:53YCK2Q5GOS6AGFDQJVHRXFRGJ

not attested not anchored not stored refs pending

Complex symmetric composition operators with automorphic symbols

Yong-Xin Gao, Ze-Hua Zhou

arxiv:1607.04801 v3 · 2016-07-16 · 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{53YCK2Q5GOS6AGFDQJVHRXFRGJ}

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	2026-05-18T01:10:14.089382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eef0256a1d33a5e018a3826a78dcb1325a5d6049fd5b91e41ef3956bf5e5ea0a

Aliases

arxiv: 1607.04801 · arxiv_version: 1607.04801v3 · doi: 10.48550/arxiv.1607.04801 · pith_short_12: 53YCK2Q5GOS6 · pith_short_16: 53YCK2Q5GOS6AGFD · pith_short_8: 53YCK2Q5

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/53YCK2Q5GOS6AGFDQJVHRXFRGJ \
  | 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: eef0256a1d33a5e018a3826a78dcb1325a5d6049fd5b91e41ef3956bf5e5ea0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "127cd8f93433ad7ac6ebce2da41b3ae007285496bfda73184e782972421a035d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-07-16T20:26:01Z",
    "title_canon_sha256": "dfcdc157cff8caaf5d10abbd9a260ca7b8f3282febe9b246466a55cb44cfa627"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.04801",
    "kind": "arxiv",
    "version": 3
  }
}