Pith Number

pith:SB64RLTQ

pith:2016:SB64RLTQHCSTHBJIOR46SHACO4

not attested not anchored not stored refs pending

Properties of $G$-martingales with finite variation and the application to $G$-Sobolev spaces

Yongsheng Song

arxiv:1607.00616 v1 · 2016-07-03 · 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{SB64RLTQHCSTHBJIOR46SHACO4}

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	2026-05-18T01:11:34.604902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

907dc8ae7038a53385287479e91c02770413547ca7ddea8aed571484ccfa7e82

Aliases

arxiv: 1607.00616 · arxiv_version: 1607.00616v1 · doi: 10.48550/arxiv.1607.00616 · pith_short_12: SB64RLTQHCST · pith_short_16: SB64RLTQHCSTHBJI · pith_short_8: SB64RLTQ

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/SB64RLTQHCSTHBJIOR46SHACO4 \
  | 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: 907dc8ae7038a53385287479e91c02770413547ca7ddea8aed571484ccfa7e82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0819c6be4832dbe60a8ae0772dc8238fcc509ff4b641d5bf2584c238fcf781cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-03T08:54:47Z",
    "title_canon_sha256": "35fc8e12bfdd4bb00f1974ab0e2b8cd4bbf1413ec5def9619ced6b2c4d98d3a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.00616",
    "kind": "arxiv",
    "version": 1
  }
}