Pith Number

pith:2QJYX2IA

pith:2026:2QJYX2IAQOXGCGE6DPQSGRR6FM

not attested not anchored not stored refs pending

Negative $K$-theory and Hodge theory

Andrew Burke, Mihnea Popa, Wanchun Shen

arxiv:2607.12672 v1 · 2026-07-14 · math.AG · 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{2QJYX2IAQOXGCGE6DPQSGRR6FM}

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	2026-07-15T01:22:11.350306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4138be90083ae61189e1be123463e2b01cfd7914e6c76b824ccfb6cb8a79fce

Aliases

arxiv: 2607.12672 · arxiv_version: 2607.12672v1 · doi: 10.48550/arxiv.2607.12672 · pith_short_12: 2QJYX2IAQOXG · pith_short_16: 2QJYX2IAQOXGCGE6 · pith_short_8: 2QJYX2IA

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/2QJYX2IAQOXGCGE6DPQSGRR6FM \
  | 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: d4138be90083ae61189e1be123463e2b01cfd7914e6c76b824ccfb6cb8a79fce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84a6d90ddd3908af48fd5d3df23b23acc57e984dab532f538f674fdd6de7ac06",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-14T11:58:58Z",
    "title_canon_sha256": "488422edf3543c3825980a7ca4cc92b98362715ced183291dfb3c8ed423e6a5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12672",
    "kind": "arxiv",
    "version": 1
  }
}