Pith Number

pith:Y525IQC5

pith:2016:Y525IQC5QQDYMUBOIFY5DLGROC

not attested not anchored not stored refs pending

Vector duality via conditional extension of dual pairs

Asgar Jamneshan, Michael Kupper, Samuel Drapeau

arxiv:1608.08709 v4 · 2016-08-31 · 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{Y525IQC5QQDYMUBOIFY5DLGROC}

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	2026-05-18T00:30:11.711998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c775d4405d840786502e4171d1acd170ace52e46db7600a8d2c497cee5d0b6cf

Aliases

arxiv: 1608.08709 · arxiv_version: 1608.08709v4 · doi: 10.48550/arxiv.1608.08709 · pith_short_12: Y525IQC5QQDY · pith_short_16: Y525IQC5QQDYMUBO · pith_short_8: Y525IQC5

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/Y525IQC5QQDYMUBOIFY5DLGROC \
  | 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: c775d4405d840786502e4171d1acd170ace52e46db7600a8d2c497cee5d0b6cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2185208b72e3c538f254e3b346c595c903979687c6462d6da1f5b5a22a1e72e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-08-31T02:27:14Z",
    "title_canon_sha256": "781420763e04377e9e9b0efc4510015aec2cd4ccd9dfa8396d4b6e6d4433961d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.08709",
    "kind": "arxiv",
    "version": 4
  }
}