Pith Number

pith:S5DCBEEZ

pith:2010:S5DCBEEZITM5T5NSPRXGE3M2TO

not attested not anchored not stored refs pending

Bar-cobar duality for operads in stable homotopy theory

Michael Ching

arxiv:1009.5034 v2 · 2010-09-25 · math.AT · 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{S5DCBEEZITM5T5NSPRXGE3M2TO}

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	2026-05-18T02:58:01.745091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

974620909944d9d9f5b27c6e626d9a9b8255f0386424f78ddd0c2b4452de9e68

Aliases

arxiv: 1009.5034 · arxiv_version: 1009.5034v2 · doi: 10.48550/arxiv.1009.5034 · pith_short_12: S5DCBEEZITM5 · pith_short_16: S5DCBEEZITM5T5NS · pith_short_8: S5DCBEEZ

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/S5DCBEEZITM5T5NSPRXGE3M2TO \
  | 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: 974620909944d9d9f5b27c6e626d9a9b8255f0386424f78ddd0c2b4452de9e68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09ecff53f19517879f5cd385986fd382c7d0e602043fef7f2833db060d554041",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-09-25T21:38:58Z",
    "title_canon_sha256": "a76e95ca501695a3022cd93d42c1096be451ff31ccb50eb182b5c785ea26a6dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5034",
    "kind": "arxiv",
    "version": 2
  }
}