Pith Number

pith:ITHUNEHC

pith:2010:ITHUNEHCTM4HCRETTLOEEOJ6X4

not attested not anchored not stored refs pending

Strict and non strict positivity of direct image bundles

Bo Berndtsson

arxiv:1002.4797 v2 · 2010-02-25 · 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{ITHUNEHCTM4HCRETTLOEEOJ6X4}

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	2026-05-18T03:42:12.193989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44cf4690e29b387144939adc42393ebf14d2f7cdb0fc58014f12bd818b64e749

Aliases

arxiv: 1002.4797 · arxiv_version: 1002.4797v2 · doi: 10.48550/arxiv.1002.4797 · pith_short_12: ITHUNEHCTM4H · pith_short_16: ITHUNEHCTM4HCRET · pith_short_8: ITHUNEHC

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/ITHUNEHCTM4HCRETTLOEEOJ6X4 \
  | 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: 44cf4690e29b387144939adc42393ebf14d2f7cdb0fc58014f12bd818b64e749

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a31b30e29c4871a4bdcee9455870bb495d7c3ad1f6d2799d91fffcb31d818b05",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-02-25T14:33:40Z",
    "title_canon_sha256": "bee7d68736075d3da332ee932e701c7d80b8bb09fa382084b9c5d270d4ed3c56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.4797",
    "kind": "arxiv",
    "version": 2
  }
}