Pith Number

pith:S7W3YAEZ

pith:2019:S7W3YAEZCPLCCEK52QF4VFA26C

not attested not anchored not stored refs pending

Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems

Julian Fischer, Stefan Neukamm

arxiv:1908.02273 v2 · 2019-08-06 · math.AP · cs.NA · math.NA · 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{S7W3YAEZCPLCCEK52QF4VFA26C}

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	2026-07-05T02:02:50.793241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97edbc009913d621115dd40bca941af0b520a89b72c89d3699a6a2e84d1a100a

Aliases

arxiv: 1908.02273 · arxiv_version: 1908.02273v2 · doi: 10.48550/arxiv.1908.02273 · pith_short_12: S7W3YAEZCPLC · pith_short_16: S7W3YAEZCPLCCEK5 · pith_short_8: S7W3YAEZ

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/S7W3YAEZCPLCCEK52QF4VFA26C \
  | 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: 97edbc009913d621115dd40bca941af0b520a89b72c89d3699a6a2e84d1a100a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a10e10245e37f0c2863982b18e500530fee3015b0aa69fd72e9ecc951133b54",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-06T17:51:20Z",
    "title_canon_sha256": "1abfd201a85be3d81af6b7e87e5f11055ee5a48daa88a03bc93fa0e19ee29723"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02273",
    "kind": "arxiv",
    "version": 2
  }
}