Pith Number

pith:ND4PHQTO

pith:2010:ND4PHQTOKDECIULOIHJQT6OCJ5

not attested not anchored not stored refs pending

Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces

Andras Vasy, Semyon Dyatlov

arxiv:1012.4391 v2 · 2010-12-20 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ND4PHQTOKDECIULOIHJQT6OCJ5}

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	2026-05-18T04:08:34.806942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68f8f3c26e50c824516e41d309f9c24f4751e871c9703e83aba61f707a87f342

Aliases

arxiv: 1012.4391 · arxiv_version: 1012.4391v2 · doi: 10.48550/arxiv.1012.4391 · pith_short_12: ND4PHQTOKDEC · pith_short_16: ND4PHQTOKDECIULO · pith_short_8: ND4PHQTO

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/ND4PHQTOKDECIULOIHJQT6OCJ5 \
  | 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: 68f8f3c26e50c824516e41d309f9c24f4751e871c9703e83aba61f707a87f342

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e315c745e31165d20fdceb002bcde3e74a27b1e5767dab6888a09e6dba444618",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-20T16:33:29Z",
    "title_canon_sha256": "824fdf816241e9a6b4d9943d7e191d1e8c4ce263fc7fd57fcb56594598bc4e20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4391",
    "kind": "arxiv",
    "version": 2
  }
}