Pith Number

pith:6GHPALUI

pith:2011:6GHPALUIC4C3OT5LEBMFHF3EZC

not attested not anchored not stored refs pending

Uniqueness of weighted Sobolev spaces with weakly differentiable weights

Jonas M. T\"olle

arxiv:1110.2888 v2 · 2011-10-13 · math.FA · 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{6GHPALUIC4C3OT5LEBMFHF3EZC}

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	2026-05-18T03:44:33.850979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f18ef02e881705b74fab2058539764c8a22f76245dbea16feb024c90a301e804

Aliases

arxiv: 1110.2888 · arxiv_version: 1110.2888v2 · doi: 10.48550/arxiv.1110.2888 · pith_short_12: 6GHPALUIC4C3 · pith_short_16: 6GHPALUIC4C3OT5L · pith_short_8: 6GHPALUI

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/6GHPALUIC4C3OT5LEBMFHF3EZC \
  | 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: f18ef02e881705b74fab2058539764c8a22f76245dbea16feb024c90a301e804

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5df609aec9c16f8a761b5e17020f0b6f8ce329a1045fdf9866f0d58dbc645cbe",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-13T10:37:16Z",
    "title_canon_sha256": "431e3c55afcb670b5cc1e72548e982dd5883d91f754184a402bbaa7169ce2c44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2888",
    "kind": "arxiv",
    "version": 2
  }
}