{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IZDJAFGTLC6QYJOFWNHBKQLTN6","short_pith_number":"pith:IZDJAFGT","canonical_record":{"source":{"id":"1008.4887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-28T19:39:25Z","cross_cats_sorted":[],"title_canon_sha256":"5182d4cf229e7bcc04fbcf5d9661f6a1810974c9343e8d6e7e9294527b7b4e61","abstract_canon_sha256":"8a9bc549ad6ac947b78331ae4944f1ab3f716075b5375bf0bc18aa4916c9988b"},"schema_version":"1.0"},"canonical_sha256":"46469014d358bd0c25c5b34e1541736f9556cb755f7699a574cc3239a55f2e37","source":{"kind":"arxiv","id":"1008.4887","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4887","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4887v1","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4887","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"IZDJAFGTLC6Q","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IZDJAFGTLC6QYJOF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IZDJAFGT","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IZDJAFGTLC6QYJOFWNHBKQLTN6","target":"record","payload":{"canonical_record":{"source":{"id":"1008.4887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-28T19:39:25Z","cross_cats_sorted":[],"title_canon_sha256":"5182d4cf229e7bcc04fbcf5d9661f6a1810974c9343e8d6e7e9294527b7b4e61","abstract_canon_sha256":"8a9bc549ad6ac947b78331ae4944f1ab3f716075b5375bf0bc18aa4916c9988b"},"schema_version":"1.0"},"canonical_sha256":"46469014d358bd0c25c5b34e1541736f9556cb755f7699a574cc3239a55f2e37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:43.492575Z","signature_b64":"CF7M08SBsPAY2JGcP0gRQo6k0dY39tp/nmTswTOB7AzZhUWwvfrgz6B04ElUNAuMMujssWECI9kAMdgUH2cLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46469014d358bd0c25c5b34e1541736f9556cb755f7699a574cc3239a55f2e37","last_reissued_at":"2026-05-18T04:41:43.492061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:43.492061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.4887","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s15vfzdF5BMYLC3F4L6TIpHUCX7BLJu3AueXusSBlhCjqrSZ4VJCM+Ny6qZGC00Xy2Ok/0ONmjslotmnHCXtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:25:45.262395Z"},"content_sha256":"edceecc40812d1fe323af3bf26f8b9c3ca0f48a9e55a9156b6680bc4c0e78f93","schema_version":"1.0","event_id":"sha256:edceecc40812d1fe323af3bf26f8b9c3ca0f48a9e55a9156b6680bc4c0e78f93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IZDJAFGTLC6QYJOFWNHBKQLTN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounded geometry, growth and topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pierre Pansu (DMA), Renata Grimaldi (DMMM)","submitted_at":"2010-08-28T19:39:25Z","abstract_excerpt":"We characterize functions which are growth types of Riemannian manifolds of bounded geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4887","kind":"arxiv","version":1},"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":"2026-05-18T04:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IfN7ghXqPUrzvavFzNuHucCqdQtSt2b4m9y0tMulhl+bcXA5/Epl1efuV2WfJyyDLJjSnfHB8A1hPsdbO7kxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:25:45.262798Z"},"content_sha256":"286439dc6160540fb7c87327fc53cda2444a424b9e9f704913ec41e4265a5c7c","schema_version":"1.0","event_id":"sha256:286439dc6160540fb7c87327fc53cda2444a424b9e9f704913ec41e4265a5c7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/bundle.json","state_url":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/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":"2026-06-10T03:25:45Z","links":{"resolver":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6","bundle":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/bundle.json","state":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IZDJAFGTLC6QYJOFWNHBKQLTN6","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":"8a9bc549ad6ac947b78331ae4944f1ab3f716075b5375bf0bc18aa4916c9988b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-28T19:39:25Z","title_canon_sha256":"5182d4cf229e7bcc04fbcf5d9661f6a1810974c9343e8d6e7e9294527b7b4e61"},"schema_version":"1.0","source":{"id":"1008.4887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4887","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4887v1","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4887","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"IZDJAFGTLC6Q","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IZDJAFGTLC6QYJOF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IZDJAFGT","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:286439dc6160540fb7c87327fc53cda2444a424b9e9f704913ec41e4265a5c7c","target":"graph","created_at":"2026-05-18T04:41:43Z","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 characterize functions which are growth types of Riemannian manifolds of bounded geometry.","authors_text":"Pierre Pansu (DMA), Renata Grimaldi (DMMM)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-28T19:39:25Z","title":"Bounded geometry, growth and topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4887","kind":"arxiv","version":1},"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:edceecc40812d1fe323af3bf26f8b9c3ca0f48a9e55a9156b6680bc4c0e78f93","target":"record","created_at":"2026-05-18T04:41:43Z","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":"8a9bc549ad6ac947b78331ae4944f1ab3f716075b5375bf0bc18aa4916c9988b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-28T19:39:25Z","title_canon_sha256":"5182d4cf229e7bcc04fbcf5d9661f6a1810974c9343e8d6e7e9294527b7b4e61"},"schema_version":"1.0","source":{"id":"1008.4887","kind":"arxiv","version":1}},"canonical_sha256":"46469014d358bd0c25c5b34e1541736f9556cb755f7699a574cc3239a55f2e37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46469014d358bd0c25c5b34e1541736f9556cb755f7699a574cc3239a55f2e37","first_computed_at":"2026-05-18T04:41:43.492061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:43.492061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CF7M08SBsPAY2JGcP0gRQo6k0dY39tp/nmTswTOB7AzZhUWwvfrgz6B04ElUNAuMMujssWECI9kAMdgUH2cLDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:43.492575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edceecc40812d1fe323af3bf26f8b9c3ca0f48a9e55a9156b6680bc4c0e78f93","sha256:286439dc6160540fb7c87327fc53cda2444a424b9e9f704913ec41e4265a5c7c"],"state_sha256":"f23511d0c3920acd59fc621c1abb58ed077368f11a948c611d75b4557c48ace1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Hxc6Dzu+fsbwNC3AnZFRQblxeIVBZTlNwY5XLu7Mq9GoaKNfx3wS/ER92ZD2HrN3iTAyR3hL8fqYdfStTbKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:25:45.268207Z","bundle_sha256":"d7ae1010d75d237f9177b774e1c2db6dd8ed926d4269be8ca92b92b67466120b"}}