Pith Number

pith:YP7VY54N

pith:2015:YP7VY54NN4MP77NSLWP7SHOINH

not attested not anchored not stored refs pending

Affine representability results in ${\mathbb A}^1$-homotopy theory I: vector bundles

Aravind Asok, Marc Hoyois, Matthias Wendt

arxiv:1506.07093 v3 · 2015-06-23 · math.AG · math.AC · math.AT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YP7VY54NN4MP77NSLWP7SHOINH}

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	2026-05-18T00:32:45.004840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3ff5c778d6f18fffdb25d9ff91dc869e33cb591d46515308315431b19d0d29b

Aliases

arxiv: 1506.07093 · arxiv_version: 1506.07093v3 · doi: 10.48550/arxiv.1506.07093 · pith_short_12: YP7VY54NN4MP · pith_short_16: YP7VY54NN4MP77NS · pith_short_8: YP7VY54N

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/YP7VY54NN4MP77NSLWP7SHOINH \
  | 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: c3ff5c778d6f18fffdb25d9ff91dc869e33cb591d46515308315431b19d0d29b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a0400d128d6fec5ef93e87b4767841f10d8374c139a16c9f908c03d36e94b7e",
    "cross_cats_sorted": [
      "math.AC",
      "math.AT",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-06-23T17:02:36Z",
    "title_canon_sha256": "04f6413d9597c2c0e25deb0905d94a5cfad02bc5dfae1ca4b9871778e2fcea5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07093",
    "kind": "arxiv",
    "version": 3
  }
}