Pith Number

pith:NTI67TQL

pith:2013:NTI67TQLYAU35HWHEXGUDZCAGW

not attested not anchored not stored refs pending

von-Neumann and Birkhoff ergodic theorems for negatively curved groups

Amos Nevo, Lewis Bowen

arxiv:1303.4109 v1 · 2013-03-17 · 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{NTI67TQLYAU35HWHEXGUDZCAGW}

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	2026-05-18T03:30:39.797808Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cd1efce0bc029be9ec725cd41e44035bee3d2ef12e437cceb305f41e023f59b

Aliases

arxiv: 1303.4109 · arxiv_version: 1303.4109v1 · doi: 10.48550/arxiv.1303.4109 · pith_short_12: NTI67TQLYAU3 · pith_short_16: NTI67TQLYAU35HWH · pith_short_8: NTI67TQL

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/NTI67TQLYAU35HWHEXGUDZCAGW \
  | 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: 6cd1efce0bc029be9ec725cd41e44035bee3d2ef12e437cceb305f41e023f59b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6f2687e89f48a788618f918d726a1b69a1c950d46085e64785655cdc4fe3e66",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-03-17T21:56:59Z",
    "title_canon_sha256": "70db012fd5a8a2580df1794d2fb9996b7972bd4d4c4003d36256410c458fbe90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.4109",
    "kind": "arxiv",
    "version": 1
  }
}