Pith Number

pith:AW576J4C

pith:2012:AW576J4C3K3LCNWBW5AREKO5JG

not attested not anchored not stored refs pending

A Compactness Theorem for Riemannian Manifolds with Boundary and Applications

Kenneth S. Knox

arxiv:1211.6210 v1 · 2012-11-27 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AW576J4C3K3LCNWBW5AREKO5JG}

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.

Cited by

1 paper in Pith

Limits of manifolds with boundary I

Receipt and verification

First computed	2026-05-18T03:39:52.251716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05bbff2782dab6b136c1b7411229dd499ab8bcefd3b0937aa13f6de42a21e79d

Aliases

arxiv: 1211.6210 · arxiv_version: 1211.6210v1 · doi: 10.48550/arxiv.1211.6210 · pith_short_12: AW576J4C3K3L · pith_short_16: AW576J4C3K3LCNWB · pith_short_8: AW576J4C

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/AW576J4C3K3LCNWBW5AREKO5JG \
  | 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: 05bbff2782dab6b136c1b7411229dd499ab8bcefd3b0937aa13f6de42a21e79d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99b14b36146b04ba718afff951c24faf744d099071b545cf33df729081f6b3af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-11-27T04:25:45Z",
    "title_canon_sha256": "a8247cc2d46b380af5307338336a34f9ff3cc6dcf5b1dd1adfb43baf39eef9d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6210",
    "kind": "arxiv",
    "version": 1
  }
}