Pith Number

pith:W67VTPSN

pith:2012:W67VTPSNQLSSRBDSXVDI34H2Z5

not attested not anchored not stored refs pending

Difference bodies in complex vector spaces

Judit Abardia

arxiv:1206.0880 v1 · 2012-06-05 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W67VTPSNQLSSRBDSXVDI34H2Z5}

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	2026-05-18T03:30:28.076241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7bf59be4d82e5288472bd468df0facf541e6a0a6434f6aa7d4a11f401e45a5d

Aliases

arxiv: 1206.0880 · arxiv_version: 1206.0880v1 · doi: 10.48550/arxiv.1206.0880 · pith_short_12: W67VTPSNQLSS · pith_short_16: W67VTPSNQLSSRBDS · pith_short_8: W67VTPSN

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/W67VTPSNQLSSRBDSXVDI34H2Z5 \
  | 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: b7bf59be4d82e5288472bd468df0facf541e6a0a6434f6aa7d4a11f401e45a5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac69e4d30df04b0f2dd9c44de26a8139c3776b4ce412fc764b18ba72aecc01d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-06-05T11:07:48Z",
    "title_canon_sha256": "e186995ecb0224e3a2dd6900a0cf55a2e1f35bfb1b826d1a8b155489eb2dcb7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0880",
    "kind": "arxiv",
    "version": 1
  }
}