Pith Number

pith:VZNXAOLJ

pith:2019:VZNXAOLJRWAUFYCGR4FZ6LLOIX

not attested not anchored not stored refs pending

A New Proof of the Gromov's Theorem on Almost Flat Manifolds

Xiaochun Rong

arxiv:1906.03377 v3 · 2019-06-08 · 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{VZNXAOLJRWAUFYCGR4FZ6LLOIX}

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

Structure of Torus Fibration Under the First Betti Number Restriction

Receipt and verification

First computed	2026-07-05T05:16:48.471157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae5b7039698d8142e0468f0b9f2d6e45c18bfb5658111e71d208e7665dd15947

Aliases

arxiv: 1906.03377 · arxiv_version: 1906.03377v3 · doi: 10.48550/arxiv.1906.03377 · pith_short_12: VZNXAOLJRWAU · pith_short_16: VZNXAOLJRWAUFYCG · pith_short_8: VZNXAOLJ

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/VZNXAOLJRWAUFYCGR4FZ6LLOIX \
  | 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: ae5b7039698d8142e0468f0b9f2d6e45c18bfb5658111e71d208e7665dd15947

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e12b1cd0041738fc52c88a223f8e6c5d9ec5bea5217292b2e54ce21778895ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-06-08T03:00:31Z",
    "title_canon_sha256": "116fa4338b59d44159ad0ffa370933093e08096ee44e1ec85d88c45c96b14ece"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.03377",
    "kind": "arxiv",
    "version": 3
  }
}