Pith Number

pith:BHJPYIOT

pith:2007:BHJPYIOTUJAXNNLSNOMTB6OSKN

not attested not anchored not stored refs pending

Weighted Sobolev L2 estimates for a class of Fourier integral operators

Michael Ruzhansky, Mitsuru Sugimoto

arxiv:0711.2868 v1 · 2007-11-19 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BHJPYIOTUJAXNNLSNOMTB6OSKN}

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	2026-05-18T04:15:50.675800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09d2fc21d3a24176b5726b9930f9d253438c7a09d1998b73bac9f4c9505b2ef1

Aliases

arxiv: 0711.2868 · arxiv_version: 0711.2868v1 · doi: 10.48550/arxiv.0711.2868 · pith_short_12: BHJPYIOTUJAX · pith_short_16: BHJPYIOTUJAXNNLS · pith_short_8: BHJPYIOT

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/BHJPYIOTUJAXNNLSNOMTB6OSKN \
  | 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: 09d2fc21d3a24176b5726b9930f9d253438c7a09d1998b73bac9f4c9505b2ef1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72ddc2f32c178e4253e70916e6f752e37fb9c53022e4c9a588abb0ab82d019e2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-11-19T09:10:01Z",
    "title_canon_sha256": "12c3fd484995c995b7ca9f5d7865ad3b7c5cc28908759ea95ae2898ad253303e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.2868",
    "kind": "arxiv",
    "version": 1
  }
}