Pith Number

pith:6LCJJHAG

pith:2015:6LCJJHAGLA5XJASXCXQQVGRKZV

not attested not anchored not stored refs pending

Symbolic dynamics on amenable groups: the entropy of generic shifts

Joshua Frisch, Omer Tamuz

arxiv:1503.06251 v1 · 2015-03-21 · 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{6LCJJHAGLA5XJASXCXQQVGRKZV}

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	2026-05-18T00:17:55.544704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2c4949c06583b74825715e10a9a2acd583ab81c22ef9cc9884b724816c55a02

Aliases

arxiv: 1503.06251 · arxiv_version: 1503.06251v1 · doi: 10.48550/arxiv.1503.06251 · pith_short_12: 6LCJJHAGLA5X · pith_short_16: 6LCJJHAGLA5XJASX · pith_short_8: 6LCJJHAG

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/6LCJJHAGLA5XJASXCXQQVGRKZV \
  | 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: f2c4949c06583b74825715e10a9a2acd583ab81c22ef9cc9884b724816c55a02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c238f69e3a19bff5ddc2b8f04284253c37f02172ce0a63a7ef402ec0be02416",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-03-21T00:32:50Z",
    "title_canon_sha256": "30c70ec99b2b0a6650ed1b4c337c6573ec8ac876a92471ff945fd86420ccb864"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06251",
    "kind": "arxiv",
    "version": 1
  }
}