Pith Number

pith:5O6FCAOV

pith:2011:5O6FCAOVNOBLPWBLRZMRH5VPNY

not attested not anchored not stored refs pending

Partial hyperbolicity on 3-dimensional nilmanifolds

Andy Hammerlindl

arxiv:1103.3724 v2 · 2011-03-18 · 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{5O6FCAOVNOBLPWBLRZMRH5VPNY}

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	2026-05-18T02:22:18.166923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebbc5101d56b82b7d82b8e5913f6af6e3486956fd1be384720cbaa6f0716f2c3

Aliases

arxiv: 1103.3724 · arxiv_version: 1103.3724v2 · doi: 10.48550/arxiv.1103.3724 · pith_short_12: 5O6FCAOVNOBL · pith_short_16: 5O6FCAOVNOBLPWBL · pith_short_8: 5O6FCAOV

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/5O6FCAOVNOBLPWBLRZMRH5VPNY \
  | 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: ebbc5101d56b82b7d82b8e5913f6af6e3486956fd1be384720cbaa6f0716f2c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04c2332fa9679bd62aee9c106e510eecdcf1df8abfe2ccd09fc98b7be133d35c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-18T22:44:20Z",
    "title_canon_sha256": "b5e6cccc37acda6d8d4996028955a463b2c735f4d1e5dfa6527453ef3eb4bdf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3724",
    "kind": "arxiv",
    "version": 2
  }
}