Pith Number

pith:TKOZRMF6

pith:2020:TKOZRMF6KRLJB44V4R7AACGGXU

not attested not anchored not stored refs pending

The Miyaoka-Yau inequality on smooth minimal models

Wanxing Liu

arxiv:2012.14096 v1 · 2020-12-28 · 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{TKOZRMF6KRLJB44V4R7AACGGXU}

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	2026-07-05T02:02:15.515474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a9d98b0be545690f395e47e0008c6bd00a2bcac7b8a55b61ae7525cf78c55d4

Aliases

arxiv: 2012.14096 · arxiv_version: 2012.14096v1 · doi: 10.48550/arxiv.2012.14096 · pith_short_12: TKOZRMF6KRLJ · pith_short_16: TKOZRMF6KRLJB44V · pith_short_8: TKOZRMF6

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/TKOZRMF6KRLJB44V4R7AACGGXU \
  | 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: 9a9d98b0be545690f395e47e0008c6bd00a2bcac7b8a55b61ae7525cf78c55d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73cf09c89e1d0a328f7d2457ddf19e879faf2e5425781d236b140ab4b11e95aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-12-28T05:00:09Z",
    "title_canon_sha256": "065bfac5f121c94c01157c0fcbf2622af20f1ae4a0b6b185a13ab7f1ea9757fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.14096",
    "kind": "arxiv",
    "version": 1
  }
}