Pith Number

pith:2F3A2TGN

pith:2009:2F3A2TGN3KXNCJG5CSKVVSZG7S

not attested not anchored not stored refs pending

Rotation Vectors for Homeomorphisms of Non-Positively Curved Manifolds

Pablo Lessa

arxiv:1001.0053 v4 · 2009-12-30 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2F3A2TGN3KXNCJG5CSKVVSZG7S}

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	2026-05-18T04:13:45.920397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1760d4ccddaaed124dd14955acb26fcbf733fd905c13ed4569af5f97122292c

Aliases

arxiv: 1001.0053 · arxiv_version: 1001.0053v4 · doi: 10.48550/arxiv.1001.0053 · pith_short_12: 2F3A2TGN3KXN · pith_short_16: 2F3A2TGN3KXNCJG5 · pith_short_8: 2F3A2TGN

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/2F3A2TGN3KXNCJG5CSKVVSZG7S \
  | 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: d1760d4ccddaaed124dd14955acb26fcbf733fd905c13ed4569af5f97122292c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa3c25a2e7f32c952efbe190ce0d5d2709b9f9718566a9a47fe3e9217acbef45",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-12-30T23:58:16Z",
    "title_canon_sha256": "576b70096ca722d5089c031724edae6d7b9864375d3335719fc5df03273fd30c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0053",
    "kind": "arxiv",
    "version": 4
  }
}