Pith Number

pith:NR4M4I5K

pith:2012:NR4M4I5KVBGDTPFJY2FYL4C5ZI

not attested not anchored not stored refs pending

Homotopy pullback of $A_n$-spaces and its applications to $A_n$-types of gauge groups

Mitsunobu Tsutaya

arxiv:1210.8252 v2 · 2012-10-31 · 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{NR4M4I5KVBGDTPFJY2FYL4C5ZI}

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	2026-05-18T01:37:21.939171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c78ce23aaa84c39bca9c68b85f05dca0988533237742bf242d4727fc0ad8d05

Aliases

arxiv: 1210.8252 · arxiv_version: 1210.8252v2 · doi: 10.48550/arxiv.1210.8252 · pith_short_12: NR4M4I5KVBGD · pith_short_16: NR4M4I5KVBGDTPFJ · pith_short_8: NR4M4I5K

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/NR4M4I5KVBGDTPFJY2FYL4C5ZI \
  | 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: 6c78ce23aaa84c39bca9c68b85f05dca0988533237742bf242d4727fc0ad8d05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c92b9ce9b0beabc2586104c16119d1a191c6fff865012bd190d31b8e696a0126",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-10-31T07:37:32Z",
    "title_canon_sha256": "cfa0007e1dbaddda64dc7e58c60c88821f18220ca3469cc73c845360ad11f6b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.8252",
    "kind": "arxiv",
    "version": 2
  }
}