Pith Number

pith:IHHL7QP5

pith:2020:IHHL7QP57PQKLJ664BKAILAJ25

not attested not anchored not stored refs pending

Invariant means on Abelian groups capture complementability of Banach spaces in their second duals

Adam P. Goucher, Tomasz Kania

arxiv:2007.02792 v2 · 2020-07-06 · 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{IHHL7QP57PQKLJ664BKAILAJ25}

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	2026-07-05T02:06:50.775100Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41cebfc1fdfbe0a5a7dee054042c09d76c4c1edaca3393ae2353dbc27f999198

Aliases

arxiv: 2007.02792 · arxiv_version: 2007.02792v2 · doi: 10.48550/arxiv.2007.02792 · pith_short_12: IHHL7QP57PQK · pith_short_16: IHHL7QP57PQKLJ66 · pith_short_8: IHHL7QP5

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/IHHL7QP57PQKLJ664BKAILAJ25 \
  | 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: 41cebfc1fdfbe0a5a7dee054042c09d76c4c1edaca3393ae2353dbc27f999198

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be89b87cc351d0aaaebf53538108b5c51f5d054cad6d0805425165553375016f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2020-07-06T14:53:26Z",
    "title_canon_sha256": "21242ebf0b27356bfef5b3c6383134e5bcb4d66e8fb81be81f3f16bc940ca03d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.02792",
    "kind": "arxiv",
    "version": 2
  }
}