Pith Number

pith:5XVSNU6R

pith:2010:5XVSNU6RJDIOMNOUEODTPZXXC2

not attested not anchored not stored refs pending

A Geometric Representation of Improper Indefinite Affine Spheres with Singularities

Marcos Craizer, Moacyr A.H.B. da Silva, Ralph C. Teixeira

arxiv:1012.2123 v2 · 2010-12-09 · 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{5XVSNU6RJDIOMNOUEODTPZXXC2}

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	2026-05-18T04:22:02.202583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edeb26d3d148d0e635d4238737e6f716b92abb3efdf0b9511f9325364b3148bd

Aliases

arxiv: 1012.2123 · arxiv_version: 1012.2123v2 · doi: 10.48550/arxiv.1012.2123 · pith_short_12: 5XVSNU6RJDIO · pith_short_16: 5XVSNU6RJDIOMNOU · pith_short_8: 5XVSNU6R

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/5XVSNU6RJDIOMNOUEODTPZXXC2 \
  | 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: edeb26d3d148d0e635d4238737e6f716b92abb3efdf0b9511f9325364b3148bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03bc6d72171f69ce14f4123c4db539645c66067d23b973c60ac88cbba5b595a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-12-09T21:10:34Z",
    "title_canon_sha256": "fadfe148ae20ef46f70f2ef7ea7f1999a746af89f2f683dd03ec2f396da9bc51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2123",
    "kind": "arxiv",
    "version": 2
  }
}