Pith Number

pith:CXUWXFMC

pith:2015:CXUWXFMCT5DKXOGEOLG6SHCNR7

not attested not anchored not stored refs pending

Realization of aperiodic subshifts and uniform densities in groups

Nathalie Aubrun, Sebasti\'an Barbieri, St\'ephan Thomass\'e

arxiv:1507.03369 v3 · 2015-07-13 · math.DS · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CXUWXFMCT5DKXOGEOLG6SHCNR7}

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	2026-05-17T23:47:49.507164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15e96b95829f46abb8c472cde91c4d8fc88e999039d0537782d8b4b2cb096384

Aliases

arxiv: 1507.03369 · arxiv_version: 1507.03369v3 · doi: 10.48550/arxiv.1507.03369 · pith_short_12: CXUWXFMCT5DK · pith_short_16: CXUWXFMCT5DKXOGE · pith_short_8: CXUWXFMC

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/CXUWXFMCT5DKXOGEOLG6SHCNR7 \
  | 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: 15e96b95829f46abb8c472cde91c4d8fc88e999039d0537782d8b4b2cb096384

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de8c60c05dc146737427ba690da7c27b7b865c27bf9e4305213197d10d25b1df",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-07-13T09:42:50Z",
    "title_canon_sha256": "bf757efc4ae51d234b846f2d65ed7f0e99f20f645c9c74949a961abfd35eb042"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03369",
    "kind": "arxiv",
    "version": 3
  }
}