Pith Number

pith:BISBWQAK

pith:2012:BISBWQAKMMIGKHJWVYZLMVBEYT

not attested not anchored not stored refs pending

Differentiable mappings on products with different degrees of differentiability in the two factors

Alexander Schmeding, Hamza Alzaareer

arxiv:1208.6510 v2 · 2012-08-31 · 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{BISBWQAKMMIGKHJWVYZLMVBEYT}

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	2026-05-18T02:16:51.516501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a241b400a6310651d36ae32b65424c4deba4f064f16f2a4a220ad2187acaff8

Aliases

arxiv: 1208.6510 · arxiv_version: 1208.6510v2 · doi: 10.48550/arxiv.1208.6510 · pith_short_12: BISBWQAKMMIG · pith_short_16: BISBWQAKMMIGKHJW · pith_short_8: BISBWQAK

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/BISBWQAKMMIGKHJWVYZLMVBEYT \
  | 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: 0a241b400a6310651d36ae32b65424c4deba4f064f16f2a4a220ad2187acaff8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc8516098131997258aad4e639d2bb2bbb45b9330eed717939ff33cdab45ee13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-31T14:38:31Z",
    "title_canon_sha256": "0f80f147992b635acc0da44db45da0a8c115cf583f1c5001a5ee1b4fd5d5a495"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.6510",
    "kind": "arxiv",
    "version": 2
  }
}