Pith Number

pith:NDWEUVMF

pith:2013:NDWEUVMFHW7H7U43DZJ7H3XDR2

not attested not anchored not stored refs pending

First-order expansion of homogenized coefficients under Bernoulli perturbations

Jean-Christophe Mourrat

arxiv:1301.7685 v3 · 2013-01-31 · math.AP · 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{NDWEUVMFHW7H7U43DZJ7H3XDR2}

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	2026-05-18T03:06:51.580671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68ec4a55853dbe7fd39b1e53f3eee38ebc3b6d09fe3b435f1f026bc2b2aa0e8e

Aliases

arxiv: 1301.7685 · arxiv_version: 1301.7685v3 · doi: 10.48550/arxiv.1301.7685 · pith_short_12: NDWEUVMFHW7H · pith_short_16: NDWEUVMFHW7H7U43 · pith_short_8: NDWEUVMF

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/NDWEUVMFHW7H7U43DZJ7H3XDR2 \
  | 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: 68ec4a55853dbe7fd39b1e53f3eee38ebc3b6d09fe3b435f1f026bc2b2aa0e8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddc0f44cfc128a8885ff8e7f3bff447a5530a1d72cd60eef3f59f0984c8862c7",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-31T17:04:38Z",
    "title_canon_sha256": "0ab1d3a3640ddd64053c07d8c845f0dbb721b3e0f7cc23b6789084d244a1ce93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.7685",
    "kind": "arxiv",
    "version": 3
  }
}