Pith Number

pith:LPOPAF4Y

pith:2017:LPOPAF4YAKHIIMZMIVH4WK5O53

not attested not anchored not stored refs pending

Hilbert Transformation and Representation of ax+b Group

Hua Liu, Pei Dang, Tao Qian

arxiv:1711.04514 v1 · 2017-11-13 · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPOPAF4YAKHIIMZMIVH4WK5O53}

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	2026-05-18T00:30:36.515407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bdcf01798028e84332c454fcb2baeeec3ecc1f803e42f8c1b3831a48989c52d

Aliases

arxiv: 1711.04514 · arxiv_version: 1711.04514v1 · doi: 10.48550/arxiv.1711.04514 · pith_short_12: LPOPAF4YAKHI · pith_short_16: LPOPAF4YAKHIIMZM · pith_short_8: LPOPAF4Y

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/LPOPAF4YAKHIIMZMIVH4WK5O53 \
  | 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: 5bdcf01798028e84332c454fcb2baeeec3ecc1f803e42f8c1b3831a48989c52d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea2d4fc4f978e974ee17ef29a3d405fb45eb9cdb7a54d61c55c198d13b773327",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2017-11-13T10:51:49Z",
    "title_canon_sha256": "02409f193b6ddc7e41b991ab8a18443deee06629511dd9a23414e370e6bf3f4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.04514",
    "kind": "arxiv",
    "version": 1
  }
}