Pith Number

pith:5AK3ZWRN

pith:2012:5AK3ZWRNAS2JXN3E6E4YZJEL7D

not attested not anchored not stored refs pending

Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces

Jan Steffen M\"uller, Ulf K\"uhn

arxiv:1205.3274 v3 · 2012-05-15 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5AK3ZWRNAS2JXN3E6E4YZJEL7D}

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	2026-05-18T03:18:06.431087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e815bcda2d04b49bb764f1398ca48bf8d6243c6a58260cbd7852f1f718e0f9f5

Aliases

arxiv: 1205.3274 · arxiv_version: 1205.3274v3 · doi: 10.48550/arxiv.1205.3274 · pith_short_12: 5AK3ZWRNAS2J · pith_short_16: 5AK3ZWRNAS2JXN3E · pith_short_8: 5AK3ZWRN

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/5AK3ZWRNAS2JXN3E6E4YZJEL7D \
  | 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: e815bcda2d04b49bb764f1398ca48bf8d6243c6a58260cbd7852f1f718e0f9f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff02df7156753a629cee10ded1aeea1b24be494a4fbada59c9057851654a67c6",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-05-15T06:59:35Z",
    "title_canon_sha256": "3cb5d7121b4d9dd6f0e64d026a0c17d5773f923878653758e0af8957aa946ea0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3274",
    "kind": "arxiv",
    "version": 3
  }
}