Pith Number

pith:HCNQZXNL

pith:2025:HCNQZXNLOFTNZXKPDTMLG5BLBU

not attested not anchored not stored refs pending

Relative topological entropy and relative mean dimension of induced factors

Kairan Liu, Yixiao Qiao

arxiv:2511.18040 v2 · 2025-11-22 · 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{HCNQZXNLOFTNZXKPDTMLG5BLBU}

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.

Cited by

1 paper in Pith

Entropies of compact subsets and supported measures

Receipt and verification

First computed	2026-07-30T01:16:38.964967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

389b0cddab7166dcdd4f1cd8b3742b0d37829b000b8369f75eaea65e034ff90e

Aliases

arxiv: 2511.18040 · arxiv_version: 2511.18040v2 · doi: 10.48550/arxiv.2511.18040 · pith_short_12: HCNQZXNLOFTN · pith_short_16: HCNQZXNLOFTNZXKP · pith_short_8: HCNQZXNL

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/HCNQZXNLOFTNZXKPDTMLG5BLBU \
  | 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: 389b0cddab7166dcdd4f1cd8b3742b0d37829b000b8369f75eaea65e034ff90e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fca34f8fd4e94038f42e6fdd99e507cc6f36d08cec60b5d27c4760f22ac69046",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-11-22T12:33:51Z",
    "title_canon_sha256": "24d508ada14778a5b96b82aee90e3b16aae949fb1f9621d0c969cec8af02d111"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.18040",
    "kind": "arxiv",
    "version": 2
  }
}