Pith Number

pith:STRGVTE6

pith:2011:STRGVTE6CH2AK7V4PWUG7EDV64

not attested not anchored not stored refs pending

Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case

Dietrich Hafner, Jean-Francois Bony

arxiv:1107.5251 v1 · 2011-07-26 · 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{STRGVTE6CH2AK7V4PWUG7EDV64}

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	2026-05-18T04:16:52.624425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94e26acc9e11f4057ebc7da86f9075f7037271f19fe79465160a9cba5b75182f

Aliases

arxiv: 1107.5251 · arxiv_version: 1107.5251v1 · doi: 10.48550/arxiv.1107.5251 · pith_short_12: STRGVTE6CH2A · pith_short_16: STRGVTE6CH2AK7V4 · pith_short_8: STRGVTE6

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/STRGVTE6CH2AK7V4PWUG7EDV64 \
  | 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: 94e26acc9e11f4057ebc7da86f9075f7037271f19fe79465160a9cba5b75182f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41185158cd276e95f6853d1672f09a7490921795b8d6688145fc530f434dee8e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-26T16:05:04Z",
    "title_canon_sha256": "360e5fe42578929772dfcabd365b7afdbc4feef4ea0eca66e4d30653398f39ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5251",
    "kind": "arxiv",
    "version": 1
  }
}