Pith Number

pith:QUI5G5XJ

pith:2016:QUI5G5XJWEJKGS4WUA2WHQPIS5

not attested not anchored not stored refs pending

Tian's invariant of the Grassmann manifold

Julien Grivaux

arxiv:1611.05263 v1 · 2016-11-16 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QUI5G5XJWEJKGS4WUA2WHQPIS5}

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	2026-05-18T00:33:27.735010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8511d376e9b112a34b96a03563c1e8977822ceae3c3da3b707d134dfe6bd814f

Aliases

arxiv: 1611.05263 · arxiv_version: 1611.05263v1 · doi: 10.48550/arxiv.1611.05263 · pith_short_12: QUI5G5XJWEJK · pith_short_16: QUI5G5XJWEJKGS4W · pith_short_8: QUI5G5XJ

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/QUI5G5XJWEJKGS4WUA2WHQPIS5 \
  | 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: 8511d376e9b112a34b96a03563c1e8977822ceae3c3da3b707d134dfe6bd814f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b49635979a6f45974d7408de7f55e20a747d1938417e813c29bf1aa8717ad09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2016-11-16T13:07:13Z",
    "title_canon_sha256": "11d4b32227ff6c9095a43b005c6942ffeccdab962e208c48a8b979ece45c24d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05263",
    "kind": "arxiv",
    "version": 1
  }
}