Pith Number

pith:JZN3DUMA

pith:2015:JZN3DUMADJF6XU3PJF5W7MS3XO

not attested not anchored not stored refs pending

Open quotients of trivial vector bundles

Jo\~ao Paulo Santos, Pedro Resende

arxiv:1510.06329 v3 · 2015-10-20 · math.FA · math.AT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JZN3DUMADJF6XU3PJF5W7MS3XO}

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	2026-05-18T00:46:04.640429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e5bb1d1801a4bebd36f497b6fb25bbbb0bb809fb0c77cc5a6f4dabafb9bb57d

Aliases

arxiv: 1510.06329 · arxiv_version: 1510.06329v3 · doi: 10.48550/arxiv.1510.06329 · pith_short_12: JZN3DUMADJF6 · pith_short_16: JZN3DUMADJF6XU3P · pith_short_8: JZN3DUMA

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/JZN3DUMADJF6XU3PJF5W7MS3XO \
  | 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: 4e5bb1d1801a4bebd36f497b6fb25bbbb0bb809fb0c77cc5a6f4dabafb9bb57d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2378cb60700a7629ce3ca65f42f478c9f83cfa9592f0f5a47fe24c88efcb30d9",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-10-20T12:30:59Z",
    "title_canon_sha256": "61319206140f1d65951b204a2a3a2863f4b7cd3ed02cc58ad04ecd15a50778e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06329",
    "kind": "arxiv",
    "version": 3
  }
}