Pith Number

pith:G5DV3TMO

pith:2013:G5DV3TMO5DBJPUSY4W54UESCQU

not attested not anchored not stored refs pending

On the duality between p-Modulus and probability measures

Giuseppe Savar\'e, Luigi Ambrosio, Simone Di Marino

arxiv:1311.1381 v2 · 2013-11-06 · math.FA · math.MG · 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{G5DV3TMO5DBJPUSY4W54UESCQU}

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	2026-05-18T01:32:10.996861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37475dcd8ee8c297d258e5bbca12428513ccae8908dbcf6685f36abe2906bfa2

Aliases

arxiv: 1311.1381 · arxiv_version: 1311.1381v2 · doi: 10.48550/arxiv.1311.1381 · pith_short_12: G5DV3TMO5DBJ · pith_short_16: G5DV3TMO5DBJPUSY · pith_short_8: G5DV3TMO

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/G5DV3TMO5DBJPUSY4W54UESCQU \
  | 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: 37475dcd8ee8c297d258e5bbca12428513ccae8908dbcf6685f36abe2906bfa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a1df351f841a02f01e3c309873674e029264d04918f3ab328740cb2c6f4e47f",
    "cross_cats_sorted": [
      "math.MG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-06T13:16:49Z",
    "title_canon_sha256": "afb659da5283add6c8350c597e82564799cea4f9f44e35606e273ae5545cf8b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1381",
    "kind": "arxiv",
    "version": 2
  }
}