Pith Number

pith:TPUL77GM

pith:2015:TPUL77GMWL5C4NAKK2LT3MA452

not attested not anchored not stored refs pending

Sublinear growth of the corrector in stochastic homogenization: Optimal stochastic estimates for slowly decaying correlations

Felix Otto, Julian Fischer

arxiv:1508.00025 v2 · 2015-07-31 · 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{TPUL77GMWL5C4NAKK2LT3MA452}

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	2026-05-18T01:32:18.327669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9be8bffcccb2fa2e340a56973db01ceea8b66f3e32c0b18aa3f7f744e91cba66

Aliases

arxiv: 1508.00025 · arxiv_version: 1508.00025v2 · doi: 10.48550/arxiv.1508.00025 · pith_short_12: TPUL77GMWL5C · pith_short_16: TPUL77GMWL5C4NAK · pith_short_8: TPUL77GM

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/TPUL77GMWL5C4NAKK2LT3MA452 \
  | 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: 9be8bffcccb2fa2e340a56973db01ceea8b66f3e32c0b18aa3f7f744e91cba66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8b3731373f5f35546e347e94a7ddbb6122fbe71b86eb36adca4f47b0116580f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-31T20:41:04Z",
    "title_canon_sha256": "39ff0ca0f12fcd6021c623fa963c9437436fe3852ecacf7ff83d3fb9f42ad719"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00025",
    "kind": "arxiv",
    "version": 2
  }
}