Pith Number

pith:OND5YFGA

pith:2018:OND5YFGA3IZFAE2N6JMWMMWIVR

not attested not anchored not stored refs pending

On the existence of vectors dual to a set of linear functionals

Shibo Liu

arxiv:1807.04012 v1 · 2018-07-11 · 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{OND5YFGA3IZFAE2N6JMWMMWIVR}

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	2026-05-18T00:10:58.291383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7347dc14c0da3250134df2596632c8ac56ee1b5de863d1b9d416b0f8c7cfe3ce

Aliases

arxiv: 1807.04012 · arxiv_version: 1807.04012v1 · doi: 10.48550/arxiv.1807.04012 · pith_short_12: OND5YFGA3IZF · pith_short_16: OND5YFGA3IZFAE2N · pith_short_8: OND5YFGA

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/OND5YFGA3IZFAE2N6JMWMMWIVR \
  | 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: 7347dc14c0da3250134df2596632c8ac56ee1b5de863d1b9d416b0f8c7cfe3ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3bfbb222ea684caee701436abbe5f73233049d223b2989d973fde5ee405a251",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-07-11T09:05:52Z",
    "title_canon_sha256": "ceab03515230f1d4cf0c7c9afa9f5906f644a19023cc58db636b047509ed9f98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.04012",
    "kind": "arxiv",
    "version": 1
  }
}