Pith Number

pith:G7MX7LXY

pith:2016:G7MX7LXYZOXWZI4KBV422FJMVX

not attested not anchored not stored refs pending

Dynamics of stochastic approximation with iterate-dependent Markov noise under verifiable conditions in compact state space with the stability of iterates not ensured

Prasenjit Karmakar, Shalabh Bhatnagar

arxiv:1601.02217 v17 · 2016-01-10 · math.DS · 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{G7MX7LXYZOXWZI4KBV422FJMVX}

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	2026-05-17T23:53:06.957272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37d97faef8cbaf6ca38a0d79ad152cadd245028700e3ed8aa41a313a89957999

Aliases

arxiv: 1601.02217 · arxiv_version: 1601.02217v17 · doi: 10.48550/arxiv.1601.02217 · pith_short_12: G7MX7LXYZOXW · pith_short_16: G7MX7LXYZOXWZI4K · pith_short_8: G7MX7LXY

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/G7MX7LXYZOXWZI4KBV422FJMVX \
  | 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: 37d97faef8cbaf6ca38a0d79ad152cadd245028700e3ed8aa41a313a89957999

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5439cb5a26557427545228ad48ee1f85abe1b72dadf28736c464c103c1bbfdf9",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-01-10T14:00:31Z",
    "title_canon_sha256": "5a76776c79e3e8d5301b3365266751ad73639301ebe4697f97ddfb3ba6df17c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.02217",
    "kind": "arxiv",
    "version": 17
  }
}