Pith Number

pith:QGATKV6X

pith:2013:QGATKV6XAKQEUDXBQ66IEMOADC

not attested not anchored not stored refs pending

A Study of Submanifolds of the Complex Grassmannian Manifold with Parallel Second Fundamental Form

Isami Koga, Yasuyuki Nagatomo

arxiv:1304.3993 v2 · 2013-04-15 · 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{QGATKV6XAKQEUDXBQ66IEMOADC}

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	2026-05-18T03:27:42.350995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81813557d702a04a0ee187bc8231c0189b8d18ab0256be00c430389411e0c6e3

Aliases

arxiv: 1304.3993 · arxiv_version: 1304.3993v2 · doi: 10.48550/arxiv.1304.3993 · pith_short_12: QGATKV6XAKQE · pith_short_16: QGATKV6XAKQEUDXB · pith_short_8: QGATKV6X

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/QGATKV6XAKQEUDXBQ66IEMOADC \
  | 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: 81813557d702a04a0ee187bc8231c0189b8d18ab0256be00c430389411e0c6e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ff074b15cbdc04c3879119e879c30568cf0d66b4336a4acdf24c5c9d801fe08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-04-15T06:06:41Z",
    "title_canon_sha256": "26621a7540e2e685be3ae9b19fd75ed0bb55d1ae7f7bf7a4e9b4546369998291"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3993",
    "kind": "arxiv",
    "version": 2
  }
}