Pith Number

pith:6TDP7Q23

pith:2018:6TDP7Q23L2LSLZ6BSRGEV3L57T

not attested not anchored not stored refs pending

Higher-degree Smoothness of Perturbations II

Gang Liu

arxiv:1809.08620 v1 · 2018-09-23 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6TDP7Q23L2LSLZ6BSRGEV3L57T}

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	2026-05-18T00:05:03.967646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4c6ffc35b5e9725e7c1944c4aed7dfcf7559eb7cbeb71d64ec05d1e5cdd0c55

Aliases

arxiv: 1809.08620 · arxiv_version: 1809.08620v1 · doi: 10.48550/arxiv.1809.08620 · pith_short_12: 6TDP7Q23L2LS · pith_short_16: 6TDP7Q23L2LSLZ6B · pith_short_8: 6TDP7Q23

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/6TDP7Q23L2LSLZ6BSRGEV3L57T \
  | 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: f4c6ffc35b5e9725e7c1944c4aed7dfcf7559eb7cbeb71d64ec05d1e5cdd0c55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99d3d05306bda4f519a0560976a17089ab95adbdcd3fac3c79913864e4a0d467",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2018-09-23T15:59:08Z",
    "title_canon_sha256": "a29baa031ca53f717c2f7a5d67eaf063cd5a2dff2d81f3cb81a33dfc1661dbb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.08620",
    "kind": "arxiv",
    "version": 1
  }
}