Pith Number

pith:43I6SGJ5

pith:2019:43I6SGJ5DVB2OODKUVNFZFHDNQ

not attested not anchored not stored refs pending

P=W for Lagrangian fibrations and degenerations of hyper-K\"ahler manifolds

Andrew Harder, Junliang Shen, Qizheng Yin, Zhiyuan Li

arxiv:1908.07510 v1 · 2019-08-20 · math.AG · 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{43I6SGJ5DVB2OODKUVNFZFHDNQ}

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	2026-07-04T23:58:36.060585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6d1e9193d1d43a7386aa55a5c94e36c384bd66fb34d4a7183ea3a03b657bb68

Aliases

arxiv: 1908.07510 · arxiv_version: 1908.07510v1 · doi: 10.48550/arxiv.1908.07510 · pith_short_12: 43I6SGJ5DVB2 · pith_short_16: 43I6SGJ5DVB2OODK · pith_short_8: 43I6SGJ5

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/43I6SGJ5DVB2OODKUVNFZFHDNQ \
  | 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: e6d1e9193d1d43a7386aa55a5c94e36c384bd66fb34d4a7183ea3a03b657bb68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8a33935fe5ee66d411e37471af4f491db2fa0dd1c5a94d330d0aa3ef8b27c42",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-08-20T17:48:54Z",
    "title_canon_sha256": "90da2164254bfb8ec3a88934958a2d1fc86aa9f98cd7cdd9843294d29bb83e17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07510",
    "kind": "arxiv",
    "version": 1
  }
}