Pith Number

pith:WJ7O4YPW

pith:2012:WJ7O4YPWFLOP32KUBN7JWXN7IX

not attested not anchored not stored refs pending

Gradient Schr\"odinger Operators, Manifolds with Density and applications

Jose M. Espinar

arxiv:1209.6162 v7 · 2012-09-27 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WJ7O4YPWFLOP32KUBN7JWXN7IX}

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	2026-05-18T02:20:29.166942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b27eee61f62adcfde9540b7e9b5dbf45d84c171fe9c0eb1841271de9f0237650

Aliases

arxiv: 1209.6162 · arxiv_version: 1209.6162v7 · doi: 10.48550/arxiv.1209.6162 · pith_short_12: WJ7O4YPWFLOP · pith_short_16: WJ7O4YPWFLOP32KU · pith_short_8: WJ7O4YPW

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/WJ7O4YPWFLOP32KUBN7JWXN7IX \
  | 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: b27eee61f62adcfde9540b7e9b5dbf45d84c171fe9c0eb1841271de9f0237650

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0d3095ba66b90479e0956bfeeb47334b4fc30ea7b5b6deb216aa791caf6c942",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-09-27T08:53:17Z",
    "title_canon_sha256": "a28c0c7cca489a9c7635a4ce2af0a928105427a124eae388da6a02d377af5089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6162",
    "kind": "arxiv",
    "version": 7
  }
}