Pith Number

pith:PZFETGKI

pith:2007:PZFETGKINFT7BMQWUBLGRNTVLG

not attested not anchored not stored refs pending

Smooth K-Theory

Thomas Schick (Georg-August-Universitaet Goettingen), Ulrich Bunke (Regensburg)

arxiv:0707.0046 v4 · 2007-06-30 · math.KT · 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{PZFETGKINFT7BMQWUBLGRNTVLG}

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	2026-05-18T04:41:06.095928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e4a4999486967f0b216a05668b675598570f91a26baa9e3681f9f003308082f

Aliases

arxiv: 0707.0046 · arxiv_version: 0707.0046v4 · doi: 10.48550/arxiv.0707.0046 · pith_short_12: PZFETGKINFT7 · pith_short_16: PZFETGKINFT7BMQW · pith_short_8: PZFETGKI

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/PZFETGKINFT7BMQWUBLGRNTVLG \
  | 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: 7e4a4999486967f0b216a05668b675598570f91a26baa9e3681f9f003308082f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2244a69881e6a73c1d4b090b0bb1eac8561a978584db55a80d4314aa3fdd59a9",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2007-06-30T07:03:25Z",
    "title_canon_sha256": "84f4a6e4307938b11c67cda1afb8285007573369a441ea0014e1cf1b73a287a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.0046",
    "kind": "arxiv",
    "version": 4
  }
}