Pith Number

pith:R6E32FF4

pith:2015:R6E32FF4IEOSEODHL5LHE7RHCS

not attested not anchored not stored refs pending

Exact triangles as modules over an $A_\infty$-category

Theo Johnson-Freyd

arxiv:1510.07275 v2 · 2015-10-25 · math.KT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R6E32FF4IEOSEODHL5LHE7RHCS}

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	2026-05-18T01:28:45.099375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f89bd14bc411d2238675f56727e2714b80b60ff5650477b903f4f655aaba6ed

Aliases

arxiv: 1510.07275 · arxiv_version: 1510.07275v2 · doi: 10.48550/arxiv.1510.07275 · pith_short_12: R6E32FF4IEOS · pith_short_16: R6E32FF4IEOSEODH · pith_short_8: R6E32FF4

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/R6E32FF4IEOSEODHL5LHE7RHCS \
  | 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: 8f89bd14bc411d2238675f56727e2714b80b60ff5650477b903f4f655aaba6ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb0d91b7c7f61e3028496dc9d74ee241a68d515baa7ba3fafbc40a727d32ceda",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2015-10-25T17:40:20Z",
    "title_canon_sha256": "56ec38e3389e1aa48a6b019e760bd1bc663e39bead06227fc9f035e32667829f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07275",
    "kind": "arxiv",
    "version": 2
  }
}