Pith Number

pith:6VL45O66

pith:2010:6VL45O66IZIMMHCMWFQ54MXDLB

not attested not anchored not stored refs pending

The basic geometry of Witt vectors, II: Spaces

James Borger

arxiv:1006.0092 v2 · 2010-06-01 · math.AG · math.CT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6VL45O66IZIMMHCMWFQ54MXDLB}

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	2026-05-18T01:24:31.132214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f557cebbde4650c61c4cb161de32e3584061dea2d2e3b2b5a0e6a36de2a84283

Aliases

arxiv: 1006.0092 · arxiv_version: 1006.0092v2 · doi: 10.48550/arxiv.1006.0092 · pith_short_12: 6VL45O66IZIM · pith_short_16: 6VL45O66IZIMMHCM · pith_short_8: 6VL45O66

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/6VL45O66IZIMMHCMWFQ54MXDLB \
  | 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: f557cebbde4650c61c4cb161de32e3584061dea2d2e3b2b5a0e6a36de2a84283

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "537750443eb35f99f4156d1f47a5cb5263d3a5f53d660522f9b308b7c779c6b5",
    "cross_cats_sorted": [
      "math.CT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-06-01T09:28:57Z",
    "title_canon_sha256": "6e08b7eb8813c3d93ca1b86f75708ce1101a8b68a1f5a98e230997d2fda462d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.0092",
    "kind": "arxiv",
    "version": 2
  }
}