Pith Number

pith:ZPBK4ACX

pith:2012:ZPBK4ACX3FJNRUVFOP2N2OAQ5N

not attested not anchored not stored refs pending

The non-parabolicity of infinite volume ends

Feliciano Vitorio, Heudson Mirandola, Marcos P. Cavalcante

arxiv:1201.6391 v3 · 2012-01-30 · 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{ZPBK4ACX3FJNRUVFOP2N2OAQ5N}

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	2026-05-18T03:28:06.275995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbc2ae0057d952d8d2a573f4dd3810eb600dfe5396fb5ceb992a67a659d5194c

Aliases

arxiv: 1201.6391 · arxiv_version: 1201.6391v3 · doi: 10.48550/arxiv.1201.6391 · pith_short_12: ZPBK4ACX3FJN · pith_short_16: ZPBK4ACX3FJNRUVF · pith_short_8: ZPBK4ACX

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/ZPBK4ACX3FJNRUVFOP2N2OAQ5N \
  | 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: cbc2ae0057d952d8d2a573f4dd3810eb600dfe5396fb5ceb992a67a659d5194c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9da615cff9f08e6152901171fde3652299432d260923e3f816951e534f56d1e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-01-30T22:17:56Z",
    "title_canon_sha256": "1469abab87b76e12e404e3a476ea87ca0c0cc45ad4a3a68b16923da18a207b11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.6391",
    "kind": "arxiv",
    "version": 3
  }
}