Pith Number

pith:W6ABQXS4

pith:2017:W6ABQXS4GP3XSHFUEZHWOPG5P5

not attested not anchored not stored refs pending

Minimizers of the sharp Log entropy on manifolds with non-negative Ricci curvature and flatness

Qi S Zhang

arxiv:1708.01049 v1 · 2017-08-03 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W6ABQXS4GP3XSHFUEZHWOPG5P5}

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	2026-05-18T00:38:40.750794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b780185e5c33f7791cb4264f673cdd7f560f9d624b65b9fcad5636bfb82b727f

Aliases

arxiv: 1708.01049 · arxiv_version: 1708.01049v1 · doi: 10.48550/arxiv.1708.01049 · pith_short_12: W6ABQXS4GP3X · pith_short_16: W6ABQXS4GP3XSHFU · pith_short_8: W6ABQXS4

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/W6ABQXS4GP3XSHFUEZHWOPG5P5 \
  | 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: b780185e5c33f7791cb4264f673cdd7f560f9d624b65b9fcad5636bfb82b727f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e32736eec6db0db0ee66591e1d113cf9ff0282c487a6458d0384a064815f5e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-08-03T08:37:53Z",
    "title_canon_sha256": "6f7b4ff5aaf7dceb5e3cd133dde28ef23a1203d9d71de93637fe47308a25f2bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.01049",
    "kind": "arxiv",
    "version": 1
  }
}