Pith Number

pith:3YMV67H4

pith:2011:3YMV67H42VYCPUC3HWJS6WHUX7

not attested not anchored not stored refs pending

Distjointness of Mobius from horocycle flows

Jean Bourgain, Peter Sarnak, Tamar Ziegler

arxiv:1110.0992 v1 · 2011-10-05 · math.NT · 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{3YMV67H42VYCPUC3HWJS6WHUX7}

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	2026-05-18T04:11:40.067036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de195f7cfcd57027d05b3d932f58f4bfd22e043e78f35e490fd98bfc143c8347

Aliases

arxiv: 1110.0992 · arxiv_version: 1110.0992v1 · doi: 10.48550/arxiv.1110.0992 · pith_short_12: 3YMV67H42VYC · pith_short_16: 3YMV67H42VYCPUC3 · pith_short_8: 3YMV67H4

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/3YMV67H42VYCPUC3HWJS6WHUX7 \
  | 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: de195f7cfcd57027d05b3d932f58f4bfd22e043e78f35e490fd98bfc143c8347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "339a5d43ce831ea3397cdfefae792749dde63fa0dcdcfb9a4c99bb7446fa270b",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-10-05T14:10:42Z",
    "title_canon_sha256": "7495fafe155398c9f2d6740b7644167ddbecc73374ad4df598ab4dbc1efc2f45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.0992",
    "kind": "arxiv",
    "version": 1
  }
}