{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:C54BV5ERM2KAHRS6LQGQE2PAQJ","short_pith_number":"pith:C54BV5ER","canonical_record":{"source":{"id":"1011.2258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-10T02:11:15Z","cross_cats_sorted":["cond-mat.mtrl-sci","cs.CG","math-ph","math.MP"],"title_canon_sha256":"0ee7bb8534b89e0c4f7aef69b092889029c1d47911ce1023ffa68e3916ac5fd3","abstract_canon_sha256":"f1530d8e22862d5954679ab3dc384c40b3b17020ef8cb9efa3fe06487e00d249"},"schema_version":"1.0"},"canonical_sha256":"17781af491669403c65e5c0d0269e0826e8f11cbfb5e9ab4fe6bc324357e8a97","source":{"kind":"arxiv","id":"1011.2258","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2258","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2258v2","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2258","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"pith_short_12","alias_value":"C54BV5ERM2KA","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"C54BV5ERM2KAHRS6","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"C54BV5ER","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:C54BV5ERM2KAHRS6LQGQE2PAQJ","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-10T02:11:15Z","cross_cats_sorted":["cond-mat.mtrl-sci","cs.CG","math-ph","math.MP"],"title_canon_sha256":"0ee7bb8534b89e0c4f7aef69b092889029c1d47911ce1023ffa68e3916ac5fd3","abstract_canon_sha256":"f1530d8e22862d5954679ab3dc384c40b3b17020ef8cb9efa3fe06487e00d249"},"schema_version":"1.0"},"canonical_sha256":"17781af491669403c65e5c0d0269e0826e8f11cbfb5e9ab4fe6bc324357e8a97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:04.037487Z","signature_b64":"CTuwZc3x8XyQUCuPN7QfWNSplTYF8wIdOt+CHfEX5CKbnLQmD5e0pGHRVDLoFEx089tYwU9NwE/Dxcu6d59rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17781af491669403c65e5c0d0269e0826e8f11cbfb5e9ab4fe6bc324357e8a97","last_reissued_at":"2026-05-18T04:33:04.036778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:04.036778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2258","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CP6J2b22zYOWU10IgCiZ9boLCqh7uPQV55NMTFKXqNayRs47pkmyGumDtZ4883Z6ZNs2g1laC290vZg9b56EBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:01:13.735571Z"},"content_sha256":"7c967ab8467fe2bc0b73cd3758f6c91db4a0c29257542415719300473c352627","schema_version":"1.0","event_id":"sha256:7c967ab8467fe2bc0b73cd3758f6c91db4a0c29257542415719300473c352627"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:C54BV5ERM2KAHRS6LQGQE2PAQJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measuring Shape with Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","cs.CG","math-ph","math.MP"],"primary_cat":"math.AT","authors_text":"Benjamin Schweinhart, Robert MacPherson","submitted_at":"2010-11-10T02:11:15Z","abstract_excerpt":"We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We demonstrate the utility and computability of this measure by applying it to branched polymers, Brownian trees, and self-avoiding random walks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2258","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nnA13VJ67UJRJ4XSgH/xvHAO/khK0l93lo9BqnS87FIPyZgP2/B+itVFeJz8Si+Guj31mKJcPOBG1EEuGaDXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:01:13.735918Z"},"content_sha256":"823ca35f8927aae308e15b388aa8b841c7a1a7e31cef5dfbf79143594abeaec0","schema_version":"1.0","event_id":"sha256:823ca35f8927aae308e15b388aa8b841c7a1a7e31cef5dfbf79143594abeaec0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C54BV5ERM2KAHRS6LQGQE2PAQJ/bundle.json","state_url":"https://pith.science/pith/C54BV5ERM2KAHRS6LQGQE2PAQJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C54BV5ERM2KAHRS6LQGQE2PAQJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T15:01:13Z","links":{"resolver":"https://pith.science/pith/C54BV5ERM2KAHRS6LQGQE2PAQJ","bundle":"https://pith.science/pith/C54BV5ERM2KAHRS6LQGQE2PAQJ/bundle.json","state":"https://pith.science/pith/C54BV5ERM2KAHRS6LQGQE2PAQJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C54BV5ERM2KAHRS6LQGQE2PAQJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:C54BV5ERM2KAHRS6LQGQE2PAQJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f1530d8e22862d5954679ab3dc384c40b3b17020ef8cb9efa3fe06487e00d249","cross_cats_sorted":["cond-mat.mtrl-sci","cs.CG","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-10T02:11:15Z","title_canon_sha256":"0ee7bb8534b89e0c4f7aef69b092889029c1d47911ce1023ffa68e3916ac5fd3"},"schema_version":"1.0","source":{"id":"1011.2258","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2258","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2258v2","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2258","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"pith_short_12","alias_value":"C54BV5ERM2KA","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"C54BV5ERM2KAHRS6","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"C54BV5ER","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:823ca35f8927aae308e15b388aa8b841c7a1a7e31cef5dfbf79143594abeaec0","target":"graph","created_at":"2026-05-18T04:33:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We demonstrate the utility and computability of this measure by applying it to branched polymers, Brownian trees, and self-avoiding random walks.","authors_text":"Benjamin Schweinhart, Robert MacPherson","cross_cats":["cond-mat.mtrl-sci","cs.CG","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-10T02:11:15Z","title":"Measuring Shape with Topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2258","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7c967ab8467fe2bc0b73cd3758f6c91db4a0c29257542415719300473c352627","target":"record","created_at":"2026-05-18T04:33:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f1530d8e22862d5954679ab3dc384c40b3b17020ef8cb9efa3fe06487e00d249","cross_cats_sorted":["cond-mat.mtrl-sci","cs.CG","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-10T02:11:15Z","title_canon_sha256":"0ee7bb8534b89e0c4f7aef69b092889029c1d47911ce1023ffa68e3916ac5fd3"},"schema_version":"1.0","source":{"id":"1011.2258","kind":"arxiv","version":2}},"canonical_sha256":"17781af491669403c65e5c0d0269e0826e8f11cbfb5e9ab4fe6bc324357e8a97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17781af491669403c65e5c0d0269e0826e8f11cbfb5e9ab4fe6bc324357e8a97","first_computed_at":"2026-05-18T04:33:04.036778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:04.036778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CTuwZc3x8XyQUCuPN7QfWNSplTYF8wIdOt+CHfEX5CKbnLQmD5e0pGHRVDLoFEx089tYwU9NwE/Dxcu6d59rDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:04.037487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2258","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c967ab8467fe2bc0b73cd3758f6c91db4a0c29257542415719300473c352627","sha256:823ca35f8927aae308e15b388aa8b841c7a1a7e31cef5dfbf79143594abeaec0"],"state_sha256":"561ade84cecad96159adf4cbbc976d810d46d4f4e10d4e156dbe635b27166521"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kwHJVankxIB44/LYI1CrKpLVMhOxTM9EQuEgDmy5GsCiwsHum7t1saK3vqoh3hgdwSjgyCKFVmtbVU3i+Gu0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:01:13.737831Z","bundle_sha256":"fa0cb98be535707c55a38443462286c6422d01344d1487276783ea304c3914bf"}}