Pith Number

pith:HRHRWP63

pith:2018:HRHRWP63POX7WBNVVDG3SXFJFO

not attested not anchored not stored refs pending

A note on Selberg's Lemma and negatively curved Hadamard manifolds

Michael Kapovich

arxiv:1808.01602 v1 · 2018-08-05 · math.GR · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HRHRWP63POX7WBNVVDG3SXFJFO}

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	2026-05-18T00:08:52.466406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c4f1b3fdb7baffb05b5a8cdb95ca92ba5f856f0af4fab6271a30b0124044f2b

Aliases

arxiv: 1808.01602 · arxiv_version: 1808.01602v1 · doi: 10.48550/arxiv.1808.01602 · pith_short_12: HRHRWP63POX7 · pith_short_16: HRHRWP63POX7WBNV · pith_short_8: HRHRWP63

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/HRHRWP63POX7WBNVVDG3SXFJFO \
  | 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: 3c4f1b3fdb7baffb05b5a8cdb95ca92ba5f856f0af4fab6271a30b0124044f2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43e9ba80f92bedf25ee83291f7fcd179f02e7842ef24575b4015f3acc9419dfa",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-08-05T12:08:59Z",
    "title_canon_sha256": "10c997c4512e69cce37f297b695215744c14b434b805fa0e4d43d10fda471377"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.01602",
    "kind": "arxiv",
    "version": 1
  }
}