Pith Number

pith:4AP4UZMV

pith:2017:4AP4UZMVH7NHZW6S3PU5XXHSVQ

not attested not anchored not stored refs pending

Normal bundles of lines on hypersurfaces

Hannah Larson

arxiv:1705.01972 v1 · 2017-05-04 · 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{4AP4UZMVH7NHZW6S3PU5XXHSVQ}

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.

Cited by

1 paper in Pith

Universal degeneracy classes for vector bundles on $\mathbb{P}^1$ bundles

Receipt and verification

First computed	2026-05-18T00:45:00.983333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e01fca65953fda7cdbd2dbe9dbdcf2ac37e418e19dc0024f5a14592df894716f

Aliases

arxiv: 1705.01972 · arxiv_version: 1705.01972v1 · doi: 10.48550/arxiv.1705.01972 · pith_short_12: 4AP4UZMVH7NH · pith_short_16: 4AP4UZMVH7NHZW6S · pith_short_8: 4AP4UZMV

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/4AP4UZMVH7NHZW6S3PU5XXHSVQ \
  | 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: e01fca65953fda7cdbd2dbe9dbdcf2ac37e418e19dc0024f5a14592df894716f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "130856a8426ce649b45faf942b258a2bcba04379ff41076fbc88561c40603dbc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-05-04T18:42:12Z",
    "title_canon_sha256": "e7f35b5a92fe2d19a563a4f565fc781ea59d32481634559f7a07bdd6642c92e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.01972",
    "kind": "arxiv",
    "version": 1
  }
}