Pith Number

pith:FVF26GHI

pith:2026:FVF26GHIHXADN5SOPKOFCLUIAQ

not attested not anchored not stored refs pending

Bosonic SPT and invertible phases and its relation to Steenrod's problem

Shota Saito, Yi Zhang, Yuji Tachikawa

arxiv:2607.14662 v1 · 2026-07-16 · hep-th · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FVF26GHIHXADN5SOPKOFCLUIAQ}

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	2026-07-17T01:21:23.774078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d4baf18e83dc036f64e7a9c512e8804053f664be96431d03acf098acd743ea3

Aliases

arxiv: 2607.14662 · arxiv_version: 2607.14662v1 · doi: 10.48550/arxiv.2607.14662 · pith_short_12: FVF26GHIHXAD · pith_short_16: FVF26GHIHXADN5SO · pith_short_8: FVF26GHI

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/FVF26GHIHXADN5SOPKOFCLUIAQ \
  | 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: 2d4baf18e83dc036f64e7a9c512e8804053f664be96431d03acf098acd743ea3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a76dcc2ad6ebf4a053e6589ab4c4d9c16971fc320042fec9e63e8cc23e894e3",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-07-16T07:30:08Z",
    "title_canon_sha256": "86bddea5885b758e52cc21efc1d96c18c2c196e9cf0cb61e5b0a4bbafa74845d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14662",
    "kind": "arxiv",
    "version": 1
  }
}