Pith Number

pith:HB5T7ZFX

pith:2011:HB5T7ZFXPXZOPJXSI37VZBPYJD

not attested not anchored not stored refs pending

Compact K\"ahler manifolds with nonpositive bisectional curvature

Gang Liu

arxiv:1112.1479 v4 · 2011-12-07 · 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{HB5T7ZFXPXZOPJXSI37VZBPYJD}

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	2026-05-18T02:53:05.019720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

387b3fe4b77df2e7a6f246ff5c85f848ddf5a888b8c1cdac574d19ce051582b5

Aliases

arxiv: 1112.1479 · arxiv_version: 1112.1479v4 · doi: 10.48550/arxiv.1112.1479 · pith_short_12: HB5T7ZFXPXZO · pith_short_16: HB5T7ZFXPXZOPJXS · pith_short_8: HB5T7ZFX

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/HB5T7ZFXPXZOPJXSI37VZBPYJD \
  | 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: 387b3fe4b77df2e7a6f246ff5c85f848ddf5a888b8c1cdac574d19ce051582b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05c75b7f5eab4f4f77b3a993d287299934857db3abb3d312273688d267ed7378",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-07T05:50:40Z",
    "title_canon_sha256": "3f26a17e90a0ed00fe1439ba247d64f57dca924a6e9ae5d3bd218bedb0007c75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1479",
    "kind": "arxiv",
    "version": 4
  }
}