Pith Number

pith:7GYH4KOB

pith:2017:7GYH4KOBUK67OVJNALDMRYF7KY

not attested not anchored not stored refs pending

Continuity and growth of free multiplicative convolution semigroups

Ping Zhong, Xiaoxue Deng

arxiv:1709.07060 v1 · 2017-09-20 · 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{7GYH4KOBUK67OVJNALDMRYF7KY}

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	2026-05-18T00:34:36.705067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9b07e29c1a2bdf7552d02c6c8e0bf5609c7b26cedaf915051acca8851f2cb5e

Aliases

arxiv: 1709.07060 · arxiv_version: 1709.07060v1 · doi: 10.48550/arxiv.1709.07060 · pith_short_12: 7GYH4KOBUK67 · pith_short_16: 7GYH4KOBUK67OVJN · pith_short_8: 7GYH4KOB

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/7GYH4KOBUK67OVJNALDMRYF7KY \
  | 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: f9b07e29c1a2bdf7552d02c6c8e0bf5609c7b26cedaf915051acca8851f2cb5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0262ee4ad7a98a307ec704f50a6e0be76c7ab0480c05956d9c027199f6f72acb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-09-20T20:05:24Z",
    "title_canon_sha256": "99a6c727f6582331ba19180e09e70ac7c4b6e84f334e38336a7682f09fb71b69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.07060",
    "kind": "arxiv",
    "version": 1
  }
}