Pith Number

pith:EK6EUY7O

pith:2015:EK6EUY7OIQ2NTU5GCSRPUAVIIM

not attested not anchored not stored refs pending

Envelope of mid-planes of a surface and some classical notions of affine differential geometry

Ady Cambraia Junior, Marcos Craizer

arxiv:1503.03019 v6 · 2015-03-10 · 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{EK6EUY7OIQ2NTU5GCSRPUAVIIM}

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	2026-05-18T00:45:01.897711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22bc4a63ee4434d9d3a614a2fa02a8430fb8b0cd10a30fd03aabdc323e6ac733

Aliases

arxiv: 1503.03019 · arxiv_version: 1503.03019v6 · doi: 10.48550/arxiv.1503.03019 · pith_short_12: EK6EUY7OIQ2N · pith_short_16: EK6EUY7OIQ2NTU5G · pith_short_8: EK6EUY7O

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/EK6EUY7OIQ2NTU5GCSRPUAVIIM \
  | 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: 22bc4a63ee4434d9d3a614a2fa02a8430fb8b0cd10a30fd03aabdc323e6ac733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "456dd1448c6f7229a1cd16c827207b2e06426dfd012ace3cc62eb697d5429180",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-03-10T18:04:42Z",
    "title_canon_sha256": "ab45782c30e0ef2e6db8020c761c19278b0c66eb0199c03c1299adf6591e7ee6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.03019",
    "kind": "arxiv",
    "version": 6
  }
}