Pith Number

pith:FPXHC6Y2

pith:2016:FPXHC6Y25XZV2YUXA2OOZ2VFZV

not attested not anchored not stored refs pending

Product space for two processes with independent increments under nonlinear expectations

Guomin Liu, Mingshang Hu, Qiang Gao, Xiaojun Ji

arxiv:1601.05507 v1 · 2016-01-21 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FPXHC6Y25XZV2YUXA2OOZ2VFZV}

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	2026-05-18T01:22:13.655160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bee717b1aedf35d6297069ceceaa5cd613edb16ad453cd15db10179ca270dd2

Aliases

arxiv: 1601.05507 · arxiv_version: 1601.05507v1 · doi: 10.48550/arxiv.1601.05507 · pith_short_12: FPXHC6Y25XZV · pith_short_16: FPXHC6Y25XZV2YUX · pith_short_8: FPXHC6Y2

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/FPXHC6Y25XZV2YUXA2OOZ2VFZV \
  | 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: 2bee717b1aedf35d6297069ceceaa5cd613edb16ad453cd15db10179ca270dd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7409dc09eac4a86c71f957fa7a2d898fcf69ef93271040027918895a875165c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-01-21T04:26:25Z",
    "title_canon_sha256": "3477abcd9800096298c9e48ca0197aae0b7956c3865ae51096a3345dc27b88a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05507",
    "kind": "arxiv",
    "version": 1
  }
}