Pith Number

pith:VLHZWV6E

pith:2011:VLHZWV6E74TRMAPGMCASIOCLZY

not attested not anchored not stored refs pending

Introduction to Vector Spaces, Vector Algebras, and Vector Geometries

Richard A. Smith

arxiv:1110.3350 v1 · 2011-10-14 · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VLHZWV6E74TRMAPGMCASIOCLZY}

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	2026-05-18T04:10:56.091838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aacf9b57c4ff271601e6608124384bce0ba0cd0d8b97aceee52a0f183d528f46

Aliases

arxiv: 1110.3350 · arxiv_version: 1110.3350v1 · doi: 10.48550/arxiv.1110.3350 · pith_short_12: VLHZWV6E74TR · pith_short_16: VLHZWV6E74TRMAPG · pith_short_8: VLHZWV6E

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/VLHZWV6E74TRMAPGMCASIOCLZY \
  | 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: aacf9b57c4ff271601e6608124384bce0ba0cd0d8b97aceee52a0f183d528f46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1909546afb6d468716ccef4e4031cb94cb3c8a2cf3a884c7005c44daff40e7df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2011-10-14T22:04:52Z",
    "title_canon_sha256": "3395aa1c881c131f9d8cb8a290d61ec3c40cb5c0e1973b0cc6b54108bd83e2ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3350",
    "kind": "arxiv",
    "version": 1
  }
}