Pith Number

pith:5Q7RUQFK

pith:2016:5Q7RUQFKQ4T3JE4ZKWBKKYD6KA

not attested not anchored not stored refs pending

Four proofs of cocompacness for Sobolev embeddings

Cyril Tintarev

arxiv:1601.04873 v1 · 2016-01-19 · 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{5Q7RUQFKQ4T3JE4ZKWBKKYD6KA}

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	2026-05-18T01:22:31.650228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec3f1a40aa8727b493995582a5607e501f6bbc52fabade5b2bdccd5abbde33ca

Aliases

arxiv: 1601.04873 · arxiv_version: 1601.04873v1 · doi: 10.48550/arxiv.1601.04873 · pith_short_12: 5Q7RUQFKQ4T3 · pith_short_16: 5Q7RUQFKQ4T3JE4Z · pith_short_8: 5Q7RUQFK

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/5Q7RUQFKQ4T3JE4ZKWBKKYD6KA \
  | 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: ec3f1a40aa8727b493995582a5607e501f6bbc52fabade5b2bdccd5abbde33ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d60860bfff41ba9bdcb9d3c01eca9a35f304bf3e3ca65aef2aa605c71ca2f4b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-01-19T11:06:05Z",
    "title_canon_sha256": "a8defb4d716c2c49297e7d7ddef4fc03ddb740a343bf7f9c96c3c07c60d5ed20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04873",
    "kind": "arxiv",
    "version": 1
  }
}