Pith Number

pith:J6DJTOIO

pith:2010:J6DJTOIOBNHDYGZN5CT74Q5SQQ

not attested not anchored not stored refs pending

Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$

Fernando Cardoso, Georgi Vodev

arxiv:1011.3919 v2 · 2010-11-17 · 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{J6DJTOIOBNHDYGZN5CT74Q5SQQ}

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	2026-05-18T04:34:08.614147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f8699b90e0b4e3c1b2de8a7fe43b2842af0eb849fdc18d4bbfe8e079ef2222c

Aliases

arxiv: 1011.3919 · arxiv_version: 1011.3919v2 · doi: 10.48550/arxiv.1011.3919 · pith_short_12: J6DJTOIOBNHD · pith_short_16: J6DJTOIOBNHDYGZN · pith_short_8: J6DJTOIO

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/J6DJTOIOBNHDYGZN5CT74Q5SQQ \
  | 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: 4f8699b90e0b4e3c1b2de8a7fe43b2842af0eb849fdc18d4bbfe8e079ef2222c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffa4538bad881ca357c2d4f0d9d1de279252219362172072689a5d3b4c4cc1dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-11-17T10:02:09Z",
    "title_canon_sha256": "9faa29d26e2f09143f8f066f4eb97867e821c99322e7f7ef469528e62794fa71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3919",
    "kind": "arxiv",
    "version": 2
  }
}