Pith Number

pith:DK4MNFYY

pith:2012:DK4MNFYYS5CVJANSM3ZJSXR5DP

not attested not anchored not stored refs pending

On compactifications and the topological dynamics of definable groups

Anand Pillay, Davide Penazzi, Jakub Gismatullin

arxiv:1212.3176 v1 · 2012-12-13 · math.LO · 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{DK4MNFYYS5CVJANSM3ZJSXR5DP}

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	2026-05-18T03:38:33.622924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ab8c6971897455481b266f2995e3d1bce16e8e42268ed86ee7ed3354070111d

Aliases

arxiv: 1212.3176 · arxiv_version: 1212.3176v1 · doi: 10.48550/arxiv.1212.3176 · pith_short_12: DK4MNFYYS5CV · pith_short_16: DK4MNFYYS5CVJANS · pith_short_8: DK4MNFYY

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/DK4MNFYYS5CVJANSM3ZJSXR5DP \
  | 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: 1ab8c6971897455481b266f2995e3d1bce16e8e42268ed86ee7ed3354070111d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85a3df7fe3b03e1167bd965c260033625dbf9dd4fff55f082325e56b3411e4aa",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2012-12-13T13:51:02Z",
    "title_canon_sha256": "5b5178a46e1618566c657617827c4bd0d05add3594bd7aa2b54df3dbaffae5d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3176",
    "kind": "arxiv",
    "version": 1
  }
}