Pith Number

pith:X6VPNTAD

pith:2019:X6VPNTAD4UKVEOKWN6PBVFZF2L

not attested not anchored not stored refs pending

Strongly Independent Matrices and Rigidity of $\times A$-Invariant Measures on $n$-Torus

Enhui Shi, Hanfeng Li, Huichi Huang, Hui Xu

arxiv:1908.02611 v2 · 2019-08-06 · 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{X6VPNTAD4UKVEOKWN6PBVFZF2L}

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	2026-07-05T02:16:11.223947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfaaf6cc03e5155239566f9e1a9725d2edc11a0c9aed7f5d08d72384bf39b853

Aliases

arxiv: 1908.02611 · arxiv_version: 1908.02611v2 · doi: 10.48550/arxiv.1908.02611 · pith_short_12: X6VPNTAD4UKV · pith_short_16: X6VPNTAD4UKVEOKW · pith_short_8: X6VPNTAD

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/X6VPNTAD4UKVEOKWN6PBVFZF2L \
  | 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: bfaaf6cc03e5155239566f9e1a9725d2edc11a0c9aed7f5d08d72384bf39b853

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9753ac7ffa03dfc90f818979bc702d0c2e9e8da9607d800acf2c723467a06ec4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-08-06T05:21:32Z",
    "title_canon_sha256": "4d447f2e499edbda9d9e0e469d0fb23ce8907c3de7553a8dbe6a0c3d749f6863"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02611",
    "kind": "arxiv",
    "version": 2
  }
}