Pith Number

pith:3ZSGCT62

pith:2017:3ZSGCT62QGJMAUOGPGDKNG4KBY

not attested not anchored not stored refs pending

Weak containment and maximal sofic approximations

Andrei Alpeev

arxiv:1706.01864 v1 · 2017-06-06 · 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{3ZSGCT62QGJMAUOGPGDKNG4KBY}

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	2026-05-18T00:42:55.718424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de64614fda8192c051c67986a69b8a0e01094b8435f0429c07552402684adab6

Aliases

arxiv: 1706.01864 · arxiv_version: 1706.01864v1 · doi: 10.48550/arxiv.1706.01864 · pith_short_12: 3ZSGCT62QGJM · pith_short_16: 3ZSGCT62QGJMAUOG · pith_short_8: 3ZSGCT62

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/3ZSGCT62QGJMAUOGPGDKNG4KBY \
  | 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: de64614fda8192c051c67986a69b8a0e01094b8435f0429c07552402684adab6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6119ffa7703f240955811fec15c6305b71216d6c0eaced8cf5b79ad6753c15ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-06-06T17:27:11Z",
    "title_canon_sha256": "f71848ec3b26fa4ed816a4aa522a92b058a9603a20e4e66dd54f94a22d966a69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.01864",
    "kind": "arxiv",
    "version": 1
  }
}