Pith Number

pith:VFWQ274K

pith:2018:VFWQ274KFNK2UODJMGIXWMV6P7

not attested not anchored not stored refs pending

Spectral gap property and strong ergodicity for groups of affine transformations of solenoids

Bachir Bekka, Camille Francini

arxiv:1802.08996 v2 · 2018-02-25 · 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{VFWQ274KFNK2UODJMGIXWMV6P7}

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	2026-05-18T00:10:10.627769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a96d0d7f8a2b55aa386961917b32be7fd762440e60f07d3e21b67fbbe3114e2d

Aliases

arxiv: 1802.08996 · arxiv_version: 1802.08996v2 · doi: 10.48550/arxiv.1802.08996 · pith_short_12: VFWQ274KFNK2 · pith_short_16: VFWQ274KFNK2UODJ · pith_short_8: VFWQ274K

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/VFWQ274KFNK2UODJMGIXWMV6P7 \
  | 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: a96d0d7f8a2b55aa386961917b32be7fd762440e60f07d3e21b67fbbe3114e2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8e0043140bbf80cf7b83f846d9ec32ef501938410aa2f3b088bb6fe0d01766e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-02-25T12:56:45Z",
    "title_canon_sha256": "510fa6acb62106c192a20f99d93fdb055dd0285214c95fcf3d15dc55c8e324ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.08996",
    "kind": "arxiv",
    "version": 2
  }
}