Pith Number

pith:F4PL3IJB

pith:2015:F4PL3IJB5V6YDFGESGACBV3V5B

not attested not anchored not stored refs pending

Isometric embeddings of polar Grassmannians and metric characterizations of their apartments

Mariusz Kwiatkowski, Mark Pankov

arxiv:1502.02873 v1 · 2015-02-10 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F4PL3IJB5V6YDFGESGACBV3V5B}

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	2026-05-18T02:27:30.591625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f1ebda121ed7d8194c4918020d775e862f32fa34ea44e7cf331fcb06529ad5b

Aliases

arxiv: 1502.02873 · arxiv_version: 1502.02873v1 · doi: 10.48550/arxiv.1502.02873 · pith_short_12: F4PL3IJB5V6Y · pith_short_16: F4PL3IJB5V6YDFGE · pith_short_8: F4PL3IJB

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/F4PL3IJB5V6YDFGESGACBV3V5B \
  | 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: 2f1ebda121ed7d8194c4918020d775e862f32fa34ea44e7cf331fcb06529ad5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0ef5204c460822c4be49b768953e36f20ef3e2cc3f38228a8d9166fce50e338",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-10T12:05:34Z",
    "title_canon_sha256": "181aabdf70194134c999a37b8c7ba4f26c9c952aa7dc05f28bda730687fcb05e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02873",
    "kind": "arxiv",
    "version": 1
  }
}