Pith Number

pith:MNZPJ6KD

pith:2015:MNZPJ6KDYXLVPJDQMYIMB7XRSK

not attested not anchored not stored refs pending

Generalized Gramians: Creating frame vectors in maximal subspaces

Feng Tian, Palle Jorgensen

arxiv:1501.07233 v1 · 2015-01-28 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MNZPJ6KDYXLVPJDQMYIMB7XRSK}

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	2026-05-18T02:28:29.824107Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6372f4f943c5d757a4706610c0fef192b16808fc96f84b2763912f5d5e218718

Aliases

arxiv: 1501.07233 · arxiv_version: 1501.07233v1 · doi: 10.48550/arxiv.1501.07233 · pith_short_12: MNZPJ6KDYXLV · pith_short_16: MNZPJ6KDYXLVPJDQ · pith_short_8: MNZPJ6KD

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/MNZPJ6KDYXLVPJDQMYIMB7XRSK \
  | 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: 6372f4f943c5d757a4706610c0fef192b16808fc96f84b2763912f5d5e218718

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd4c6cdb6167438f52ffd61db2067bd6863ea7915c7f2aa72b7b0bd8e5312a6c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-01-28T18:58:38Z",
    "title_canon_sha256": "945d10729a2b14bb44a83ee7d4b80d16f17b415a1e31c3ad060aa3df85d89ed1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07233",
    "kind": "arxiv",
    "version": 1
  }
}