Pith Number

pith:6ZQ4W7HO

pith:2015:6ZQ4W7HOA27LZS7SFSSPXXXE2X

not attested not anchored not stored refs pending

Higher Euler characteristics

Niranjan Ramachandran

arxiv:1509.05089 v1 · 2015-09-17 · math.KT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6ZQ4W7HOA27LZS7SFSSPXXXE2X}

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	2026-05-18T01:32:49.939385Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f661cb7cee06bebccbf22ca4fbdee4d5f3481d5c200de55075bcac62972ffae9

Aliases

arxiv: 1509.05089 · arxiv_version: 1509.05089v1 · doi: 10.48550/arxiv.1509.05089 · pith_short_12: 6ZQ4W7HOA27L · pith_short_16: 6ZQ4W7HOA27LZS7S · pith_short_8: 6ZQ4W7HO

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/6ZQ4W7HOA27LZS7SFSSPXXXE2X \
  | 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: f661cb7cee06bebccbf22ca4fbdee4d5f3481d5c200de55075bcac62972ffae9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6efd63b1842a8305f04ff16686111ea4f4708678451be3f95781a2ec8ffbe00e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2015-09-17T00:46:54Z",
    "title_canon_sha256": "082a727e9d4230d3d1cf42a1abdf8f5d05c22e4b3cd56f6137579e7cb33892ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05089",
    "kind": "arxiv",
    "version": 1
  }
}