Pith Number

pith:QKZGSQKL

pith:2012:QKZGSQKLWMFPWWR45KT2CKBR43

not attested not anchored not stored refs pending

Invariant distributions and cohomology for geodesic flows and higher cohomology of higher-rank Anosov actions

Felipe A. Ramirez

arxiv:1210.0475 v4 · 2012-10-01 · 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{QKZGSQKLWMFPWWR45KT2CKBR43}

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	2026-05-18T03:18:49.822433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82b269414bb30afb5a3ceaa7a12831e6d39156dd532ede2d15b727a406617a4f

Aliases

arxiv: 1210.0475 · arxiv_version: 1210.0475v4 · doi: 10.48550/arxiv.1210.0475 · pith_short_12: QKZGSQKLWMFP · pith_short_16: QKZGSQKLWMFPWWR4 · pith_short_8: QKZGSQKL

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/QKZGSQKLWMFPWWR45KT2CKBR43 \
  | 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: 82b269414bb30afb5a3ceaa7a12831e6d39156dd532ede2d15b727a406617a4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ca0829d73c71329838c4c1009f284bd5eb4cf0c42f26e475d58a8a422f80b2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-01T17:18:12Z",
    "title_canon_sha256": "2294f9671b4cf540976d870281429b7417f9ecd0d44b182b16f8228f094f1e0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0475",
    "kind": "arxiv",
    "version": 4
  }
}