Pith Number

pith:647J4PEY

pith:2005:647J4PEYKEA3FZGODWRCRMOOLH

not attested not anchored not stored refs pending

Hodge metrics and positivity of direct images

Christophe Mourougane (IMJ), Shigeharu Takayama

arxiv:math/0505324 v2 · 2005-05-16 · math.AG · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{647J4PEYKEA3FZGODWRCRMOOLH}

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	2026-05-18T00:15:08.014887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f73e9e3c985101b2e4ce1da228b1ce59d9add8280e1d3d144201792b240c615e

Aliases

arxiv: math/0505324 · arxiv_version: math/0505324v2 · doi: 10.48550/arxiv.math/0505324 · pith_short_12: 647J4PEYKEA3 · pith_short_16: 647J4PEYKEA3FZGO · pith_short_8: 647J4PEY

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/647J4PEYKEA3FZGODWRCRMOOLH \
  | 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: f73e9e3c985101b2e4ce1da228b1ce59d9add8280e1d3d144201792b240c615e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17f88eb7c395a57b34a989eaab38a48185fb3e95ca29cb9f265a0002b291c5fb",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2005-05-16T12:36:36Z",
    "title_canon_sha256": "cfc0c6ebcf099df17c0098567ecf4ee14accf38604fd22d37cd1a47e0ab6ae60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505324",
    "kind": "arxiv",
    "version": 2
  }
}