Pith Number

pith:7NMGQNOZ

pith:2011:7NMGQNOZUXYHFFMUQL3FVUV2S4

not attested not anchored not stored refs pending

On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators

Alex Iosevich, Eyvindur Palsson, Mihalis Mourgoglou

arxiv:1110.6792 v1 · 2011-10-31 · math.CA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7NMGQNOZUXYHFFMUQL3FVUV2S4}

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	2026-05-18T04:09:54.185733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb586835d9a5f072959482f65ad2ba971d7a10926f10529cd580f8e63652a695

Aliases

arxiv: 1110.6792 · arxiv_version: 1110.6792v1 · doi: 10.48550/arxiv.1110.6792 · pith_short_12: 7NMGQNOZUXYH · pith_short_16: 7NMGQNOZUXYHFFMU · pith_short_8: 7NMGQNOZ

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/7NMGQNOZUXYHFFMUQL3FVUV2S4 \
  | 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: fb586835d9a5f072959482f65ad2ba971d7a10926f10529cd580f8e63652a695

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "689231380cee570956cffc51728707a18d97a7a69143a4b452808428208352c9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-10-31T13:41:54Z",
    "title_canon_sha256": "9c2435ac5bbf48e47a3036938178be7e022caf8665ec53e7f77ae7264ec1f5c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6792",
    "kind": "arxiv",
    "version": 1
  }
}