Pith Number

pith:VTWR3DCY

pith:2008:VTWR3DCYYJ2J6EV6X6SJOTVZUL

not attested not anchored not stored refs pending

Simple homotopy invariance of higher signatures

Renyi Ma

arxiv:0808.2859 v5 · 2008-08-21 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VTWR3DCYYJ2J6EV6X6SJOTVZUL}

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	2026-05-18T03:56:08.845514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aced1d8c58c2749f12bebfa4974eb9a2fd32a51bd9649216b4f41dcf34bd773e

Aliases

arxiv: 0808.2859 · arxiv_version: 0808.2859v5 · doi: 10.48550/arxiv.0808.2859 · pith_short_12: VTWR3DCYYJ2J · pith_short_16: VTWR3DCYYJ2J6EV6 · pith_short_8: VTWR3DCY

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/VTWR3DCYYJ2J6EV6X6SJOTVZUL \
  | 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: aced1d8c58c2749f12bebfa4974eb9a2fd32a51bd9649216b4f41dcf34bd773e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "877d69550cad80b9751548d1db866a350c88ea6864e1bd53f2cc1f54d186b3e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-08-21T04:48:28Z",
    "title_canon_sha256": "2550f24f1856e1dfe94adb1e6baab495428ae93f6e81eafa2e525ce6832ab863"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.2859",
    "kind": "arxiv",
    "version": 5
  }
}