Pith Number

pith:EIFNFNPY

pith:2007:EIFNFNPYDPYFY6DWQX5VHMH7V5

not attested not anchored not stored refs pending

Comparing composites of left and right derived functors

Michael Shulman

arxiv:0706.2868 v2 · 2007-06-19 · math.CT · 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{EIFNFNPYDPYFY6DWQX5VHMH7V5}

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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.

Cited by

1 paper in Pith

Transposing cartesian and other structure in double categories

Receipt and verification

First computed	2026-05-18T04:27:48.037953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

220ad2b5f81bf05c787685fb53b0ffaf63661ee5cf09bce39b22b22c26110cc2

Aliases

arxiv: 0706.2868 · arxiv_version: 0706.2868v2 · doi: 10.48550/arxiv.0706.2868 · pith_short_12: EIFNFNPYDPYF · pith_short_16: EIFNFNPYDPYFY6DW · pith_short_8: EIFNFNPY

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/EIFNFNPYDPYFY6DWQX5VHMH7V5 \
  | 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: 220ad2b5f81bf05c787685fb53b0ffaf63661ee5cf09bce39b22b22c26110cc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dfe6bb4bb5728a0019b90183a757b0e222399aaf229d5d0fa52b4c09fe5bf22",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2007-06-19T20:18:05Z",
    "title_canon_sha256": "806e06c78b8df93cd441aa70ff8518d3a85b67ce369dfa232901a1b10ac3d8b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.2868",
    "kind": "arxiv",
    "version": 2
  }
}