Pith Number

pith:QBGDF7FX

pith:2016:QBGDF7FXZVTQ5TCTP3BWBV4L6M

not attested not anchored not stored refs pending

Approaching bilinear multipliers via a functional calculus

B{\l}a\.zej Wr\'obel

arxiv:1609.01083 v1 · 2016-09-05 · 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{QBGDF7FXZVTQ5TCTP3BWBV4L6M}

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	2026-05-18T01:06:19.087969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

804c32fcb7cd670ecc537ec360d78bf3101b6be5f36d4b81db0d2f74e2fd83d1

Aliases

arxiv: 1609.01083 · arxiv_version: 1609.01083v1 · doi: 10.48550/arxiv.1609.01083 · pith_short_12: QBGDF7FXZVTQ · pith_short_16: QBGDF7FXZVTQ5TCT · pith_short_8: QBGDF7FX

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/QBGDF7FXZVTQ5TCTP3BWBV4L6M \
  | 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: 804c32fcb7cd670ecc537ec360d78bf3101b6be5f36d4b81db0d2f74e2fd83d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b16c541f61c23fe2197169909b17a4b9fc8c701ed07df65bd72bc5667dde9ae5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-09-05T10:26:42Z",
    "title_canon_sha256": "3dc92e552463d9c7a7482ac2744cc132fb4b1c1f66a04af8323e03f469959af7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01083",
    "kind": "arxiv",
    "version": 1
  }
}