Pith Number

pith:T3KZVATA

pith:2019:T3KZVATAXQGFZW6DKTE333PNJC

not attested not anchored not stored refs pending

Tight trees and model geometries of surface bundles over graphs

Mahan Mj

arxiv:1901.02170 v2 · 2019-01-08 · 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{T3KZVATAXQGFZW6DKTE333PNJC}

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.

Cited by

1 paper in Pith

Cubulating Surface-by-free Groups

Receipt and verification

First computed	2026-07-05T01:16:37.941656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ed59a8260bc0c5cdbc354c9bdeded48b11e03edb462985a00930bedc1565427

Aliases

arxiv: 1901.02170 · arxiv_version: 1901.02170v2 · doi: 10.48550/arxiv.1901.02170 · pith_short_12: T3KZVATAXQGF · pith_short_16: T3KZVATAXQGFZW6D · pith_short_8: T3KZVATA

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/T3KZVATAXQGFZW6DKTE333PNJC \
  | 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: 9ed59a8260bc0c5cdbc354c9bdeded48b11e03edb462985a00930bedc1565427

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "979b512d5c8ed0111a7f54811b8e203ff328dab6beece9fb54eaa990fea8b94a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-01-08T06:29:30Z",
    "title_canon_sha256": "f729ca0b18e339fddf68384a66f671dc1294558192dc75dfb564aaf036454af6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.02170",
    "kind": "arxiv",
    "version": 2
  }
}