Pith Number

pith:2ZM2KN45

pith:2013:2ZM2KN45ISHXVEIWRCQUP2OVQJ

not attested not anchored not stored refs pending

Sharp capacity estimates for annuli in weighted R^n and in metric spaces

Anders Bj\"orn, Jana Bj\"orn, Juha Lehrb\"ack

arxiv:1312.1668 v1 · 2013-12-05 · 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{2ZM2KN45ISHXVEIWRCQUP2OVQJ}

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	2026-05-18T00:36:48.208538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d659a5379d448f7a911688a147e9d58247be2c0d7875667470fe617586607dc2

Aliases

arxiv: 1312.1668 · arxiv_version: 1312.1668v1 · doi: 10.48550/arxiv.1312.1668 · pith_short_12: 2ZM2KN45ISHX · pith_short_16: 2ZM2KN45ISHXVEIW · pith_short_8: 2ZM2KN45

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/2ZM2KN45ISHXVEIWRCQUP2OVQJ \
  | 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: d659a5379d448f7a911688a147e9d58247be2c0d7875667470fe617586607dc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "513c47fdca00413a658166516836c5ba51ca3ba66f2f3290538f844a26aa2943",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-12-05T20:08:05Z",
    "title_canon_sha256": "54f718685e470350928e44b9eae92788faa785cbc9481d13f6a3d758759958b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1668",
    "kind": "arxiv",
    "version": 1
  }
}