Pith Number

pith:KAQAWPGM

pith:2010:KAQAWPGMTDCESYS2IVSAOUYVRN

not attested not anchored not stored refs pending

Relative Index Pairing and Odd Index Theorem for Even Dimensional Manifolds

Zhizhang Xie

arxiv:1001.4822 v3 · 2010-01-27 · math.DG · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KAQAWPGMTDCESYS2IVSAOUYVRN}

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	2026-05-18T04:39:28.817712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50200b3ccc98c449625a45640753158b74c35a0389e552d772efd036bb404f6f

Aliases

arxiv: 1001.4822 · arxiv_version: 1001.4822v3 · doi: 10.48550/arxiv.1001.4822 · pith_short_12: KAQAWPGMTDCE · pith_short_16: KAQAWPGMTDCESYS2 · pith_short_8: KAQAWPGM

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/KAQAWPGMTDCESYS2IVSAOUYVRN \
  | 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: 50200b3ccc98c449625a45640753158b74c35a0389e552d772efd036bb404f6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6475c814c805df9053802faa05b035c532ef6d1ccbe71d7563511ef77ea0f003",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-01-27T15:54:38Z",
    "title_canon_sha256": "c48c5b2fd3ddd50ab51da20733221762638e37f87e35e44805000b826f281bde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.4822",
    "kind": "arxiv",
    "version": 3
  }
}