Pith Number

pith:Q5MN7RSP

pith:2018:Q5MN7RSPF7AO725EJUVGE4BQ4C

not attested not anchored not stored refs pending

A Generalization of Exponential Class and its Applications

Chao Liu, Hong Tian, Hongya Gao

arxiv:1812.07843 v1 · 2018-12-19 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q5MN7RSPF7AO725EJUVGE4BQ4C}

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	2026-05-17T23:57:55.789323Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8758dfc64f2fc0efeba44d2a627030e083f04efe57bb7255970fd6e769502d27

Aliases

arxiv: 1812.07843 · arxiv_version: 1812.07843v1 · doi: 10.48550/arxiv.1812.07843 · pith_short_12: Q5MN7RSPF7AO · pith_short_16: Q5MN7RSPF7AO725E · pith_short_8: Q5MN7RSP

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/Q5MN7RSPF7AO725EJUVGE4BQ4C \
  | 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: 8758dfc64f2fc0efeba44d2a627030e083f04efe57bb7255970fd6e769502d27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19aee5d37e4980b1d17dadb868ff3f326c741ba025d786a7d9c65d2323081f77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-12-19T09:47:26Z",
    "title_canon_sha256": "e583a2c2b8311e282ad3cdb6c073024927bf1aea667f6b2606827b068c589951"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.07843",
    "kind": "arxiv",
    "version": 1
  }
}