Pith Number

pith:GRB6AUML

pith:2026:GRB6AUML43QQ5KWK2GK5WQCMHM

not attested not anchored not stored refs pending

Analytic index theory and spectral flow in real Hilbert $C^*$-modules

Adam Rennie, Alan L. Carey, Chris Bourne, Koen van den Dungen

arxiv:2606.31322 v1 · 2026-06-30 · math.OA · 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{GRB6AUML43QQ5KWK2GK5WQCMHM}

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	2026-07-01T01:17:59.145333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3443e0518be6e10eaacad195db404c3b172ff0a8ec64dad01c416487e2427c29

Aliases

arxiv: 2606.31322 · arxiv_version: 2606.31322v1 · doi: 10.48550/arxiv.2606.31322 · pith_short_12: GRB6AUML43QQ · pith_short_16: GRB6AUML43QQ5KWK · pith_short_8: GRB6AUML

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/GRB6AUML43QQ5KWK2GK5WQCMHM \
  | 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: 3443e0518be6e10eaacad195db404c3b172ff0a8ec64dad01c416487e2427c29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a810f03b3a54368f7313785474f8bd4093eb23f6690bc90d5e10c0317dea137",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-06-30T08:27:21Z",
    "title_canon_sha256": "3006a49c81f76aa7de005bdd7d0565ffe27a7da931e5bf79ce95931ab449ca9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31322",
    "kind": "arxiv",
    "version": 1
  }
}