Pith Number

pith:ZFR7M3JJ

pith:2022:ZFR7M3JJMMQPDYWRE3YXTPO2VS

not attested not anchored not stored refs pending

On variational principle for upper metric mean dimension with potential

Ercai Chen, Rui Yang, Xiaoyao Zhou

arxiv:2207.01901 v4 · 2022-07-05 · 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{ZFR7M3JJMMQPDYWRE3YXTPO2VS}

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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

Variational principle for random pressure function

Receipt and verification

First computed	2026-07-05T09:54:22.324426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c963f66d296320f1e2d126f179bddaac9523d7c8573aac393a7c0cf8e3a0a532

Aliases

arxiv: 2207.01901 · arxiv_version: 2207.01901v4 · doi: 10.48550/arxiv.2207.01901 · pith_short_12: ZFR7M3JJMMQP · pith_short_16: ZFR7M3JJMMQPDYWR · pith_short_8: ZFR7M3JJ

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/ZFR7M3JJMMQPDYWRE3YXTPO2VS \
  | 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: c963f66d296320f1e2d126f179bddaac9523d7c8573aac393a7c0cf8e3a0a532

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e013ba4bc03f02f95fa443cb612c6908e32d8a6651648b8bc2c039d762708f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2022-07-05T09:02:03Z",
    "title_canon_sha256": "88d6bcbf6181c4b1cc105377e3d8a1159152ef1401326adc7221a5261fa80193"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2207.01901",
    "kind": "arxiv",
    "version": 4
  }
}