Pith Number

pith:VMRGV7S2

pith:2016:VMRGV7S2FUQHT5PL6C2Z2IVGS4

not attested not anchored not stored refs pending

Gradient flow for the Boltzmann entropy and Cheeger's energy on time-dependent metric measure spaces

Eva Kopfer

arxiv:1611.09522 v3 · 2016-11-29 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMRGV7S2FUQHT5PL6C2Z2IVGS4}

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	2026-05-18T00:27:02.818489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab226afe5a2d2079f5ebf0b59d22a69706c2fd64f441991b747f716ded5e36ac

Aliases

arxiv: 1611.09522 · arxiv_version: 1611.09522v3 · doi: 10.48550/arxiv.1611.09522 · pith_short_12: VMRGV7S2FUQH · pith_short_16: VMRGV7S2FUQHT5PL · pith_short_8: VMRGV7S2

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/VMRGV7S2FUQHT5PL6C2Z2IVGS4 \
  | 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: ab226afe5a2d2079f5ebf0b59d22a69706c2fd64f441991b747f716ded5e36ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dfe90e350ae10061b79623268b656d1f520540dcfcad7a926ca610178b7610e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-29T08:23:06Z",
    "title_canon_sha256": "9ecd89eedb424b5871a2efa0e4e158a998b3a4ea3395114eca739ea86e495d41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09522",
    "kind": "arxiv",
    "version": 3
  }
}