Pith Number

pith:K5VN4LQG

pith:2009:K5VN4LQGVLI7KKPFL5NWIFOXCZ

not attested not anchored not stored refs pending

Strichartz estimates without loss on manifolds with hyperbolic trapped geodesics

Andrew Hassell, Colin Guillarmou (JAD), Nicolas Burq (LM-Orsay)

arxiv:0907.3545 v2 · 2009-07-21 · 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{K5VN4LQGVLI7KKPFL5NWIFOXCZ}

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	2026-05-18T04:27:15.227770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

576ade2e06aad1f529e55f5b6415d7166e5ab0de5fd223355690724e25745143

Aliases

arxiv: 0907.3545 · arxiv_version: 0907.3545v2 · doi: 10.48550/arxiv.0907.3545 · pith_short_12: K5VN4LQGVLI7 · pith_short_16: K5VN4LQGVLI7KKPF · pith_short_8: K5VN4LQG

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/K5VN4LQGVLI7KKPFL5NWIFOXCZ \
  | 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: 576ade2e06aad1f529e55f5b6415d7166e5ab0de5fd223355690724e25745143

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76b6c9953d6c0d35343a2b9c0cfd6b59ef0b610ac89b00b42d3fb0604dcb2dfc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-07-21T05:57:16Z",
    "title_canon_sha256": "755ab5df368fbc3d0f66dac9eb114b0ff4e19f33c84359cb169a58cf28fcd0b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.3545",
    "kind": "arxiv",
    "version": 2
  }
}