Pith Number

pith:KITTRM22

pith:2021:KITTRM22T3BSJYJCGPYYV6G7WW

not attested not anchored not stored refs pending

A proof of Gromov's cube inequality on scalar curvature

Guoliang Yu, Jinmin Wang, Zhizhang Xie

arxiv:2105.12054 v4 · 2021-05-25 · 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{KITTRM22T3BSJYJCGPYYV6G7WW}

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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

Gap phenomenon for scalar curvature

Receipt and verification

First computed	2026-07-05T06:03:51.570345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

522738b35a9ec324e12233f18af8dfb58a3f44c40f661365042eb523864f2ea5

Aliases

arxiv: 2105.12054 · arxiv_version: 2105.12054v4 · doi: 10.48550/arxiv.2105.12054 · pith_short_12: KITTRM22T3BS · pith_short_16: KITTRM22T3BSJYJC · pith_short_8: KITTRM22

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/KITTRM22T3BSJYJCGPYYV6G7WW \
  | 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: 522738b35a9ec324e12233f18af8dfb58a3f44c40f661365042eb523864f2ea5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dacf81a9d271b610a02ca765c065cdb556ca66c87e3deb3d24ceee8dc467ff3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-05-25T16:33:57Z",
    "title_canon_sha256": "e8c7527909b7c86a4eff70b9ed6b529d4cefc29d93f9cdb9e92636cd59b906fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.12054",
    "kind": "arxiv",
    "version": 4
  }
}