Pith Number

pith:O7GEHRRJ

pith:2015:O7GEHRRJPWSWC3CX2L5S2U6J5Z

not attested not anchored not stored refs pending

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in $\mathcal{A}_{\alpha}\left(M\right)$ for arbitrary Liouvillean number $\alpha$

Philipp Kunde, Roland Gunesch

arxiv:1512.00075 v1 · 2015-11-30 · 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{O7GEHRRJPWSWC3CX2L5S2U6J5Z}

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	2026-05-18T01:25:32.829326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77cc43c6297da5616c57d2fb2d53c9ee4a74612f0e03dee3f8326a1b2685ea0a

Aliases

arxiv: 1512.00075 · arxiv_version: 1512.00075v1 · doi: 10.48550/arxiv.1512.00075 · pith_short_12: O7GEHRRJPWSW · pith_short_16: O7GEHRRJPWSWC3CX · pith_short_8: O7GEHRRJ

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/O7GEHRRJPWSWC3CX2L5S2U6J5Z \
  | 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: 77cc43c6297da5616c57d2fb2d53c9ee4a74612f0e03dee3f8326a1b2685ea0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8361dc1bc26568b1f2c5ebf37c5c8b9a9056cd8be672767189040b0f7b9c1d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-11-30T22:32:22Z",
    "title_canon_sha256": "0778c1b0bd27405b8dceca6b2cd3e4f53b303d37940f3cd155a494f41e091966"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00075",
    "kind": "arxiv",
    "version": 1
  }
}