Pith Number

pith:7TSDMCEP

pith:2012:7TSDMCEPY3O25FRAHZ4TAG6TND

not attested not anchored not stored refs pending

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

Luigi Ambrosio, Maria Colombo, Simone Di Marino

arxiv:1212.3779 v1 · 2012-12-16 · 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{7TSDMCEPY3O25FRAHZ4TAG6TND}

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.

Cited by

2 papers in Pith

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs

Receipt and verification

First computed	2026-05-18T03:38:22.414965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fce436088fc6ddae96203e79301bd368d22940e465f9e012be5dfeeb01350775

Aliases

arxiv: 1212.3779 · arxiv_version: 1212.3779v1 · doi: 10.48550/arxiv.1212.3779 · pith_short_12: 7TSDMCEPY3O2 · pith_short_16: 7TSDMCEPY3O25FRA · pith_short_8: 7TSDMCEP

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/7TSDMCEPY3O25FRAHZ4TAG6TND \
  | 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: fce436088fc6ddae96203e79301bd368d22940e465f9e012be5dfeeb01350775

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1a5acd733c1a0c4a24c9f2191d22fe85c4a5b3dd646b6c8530a48639f3bf4ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-16T11:55:59Z",
    "title_canon_sha256": "23d0ed1fceae65b582daca076f67286471c8eff87281f6bb4a14d6e6982d0468"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3779",
    "kind": "arxiv",
    "version": 1
  }
}