Pith Number

pith:6PRPA5S6

pith:2015:6PRPA5S6T53TTJJGQMQ2GJ5DKK

not attested not anchored not stored refs pending

Mesoscopic higher regularity and subadditivity in elliptic homogenization

Jean-Christophe Mourrat, Scott Armstrong, Tuomo Kuusi

arxiv:1507.06935 v3 · 2015-07-24 · 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{6PRPA5S6T53TTJJGQMQ2GJ5DKK}

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	2026-05-18T01:12:08.310122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3e2f0765e9f7739a5268321a327a352a9f6c6b87d5f41aff86159d873c3159f

Aliases

arxiv: 1507.06935 · arxiv_version: 1507.06935v3 · doi: 10.48550/arxiv.1507.06935 · pith_short_12: 6PRPA5S6T53T · pith_short_16: 6PRPA5S6T53TTJJG · pith_short_8: 6PRPA5S6

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/6PRPA5S6T53TTJJGQMQ2GJ5DKK \
  | 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: f3e2f0765e9f7739a5268321a327a352a9f6c6b87d5f41aff86159d873c3159f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9ae91b9a86a7f64683077798a581b23128ec040dd482fcfe4b2b95e3f6c8990",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-24T18:09:59Z",
    "title_canon_sha256": "e2362f1d6f2445c41afb0670ac452baff7c56a18d78eaa53e89aeb60b9a3e5f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06935",
    "kind": "arxiv",
    "version": 3
  }
}