{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:M6HOQGNRJS32CH55C6QUXTUHCN","short_pith_number":"pith:M6HOQGNR","canonical_record":{"source":{"id":"1603.07654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-24T16:48:10Z","cross_cats_sorted":[],"title_canon_sha256":"fd40bda3a2a810eaa7027452ec98049befb94c7f931d8c1fb374539b47551417","abstract_canon_sha256":"c447cdce036cf058857b406e9195ce2130169af4579c8b0a2ff99db4616e798c"},"schema_version":"1.0"},"canonical_sha256":"678ee819b14cb7a11fbd17a14bce87136cb98ead8bec320b3f3678b0a80b62bc","source":{"kind":"arxiv","id":"1603.07654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07654","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07654v2","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07654","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"M6HOQGNRJS32","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6HOQGNRJS32CH55","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6HOQGNR","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:M6HOQGNRJS32CH55C6QUXTUHCN","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-24T16:48:10Z","cross_cats_sorted":[],"title_canon_sha256":"fd40bda3a2a810eaa7027452ec98049befb94c7f931d8c1fb374539b47551417","abstract_canon_sha256":"c447cdce036cf058857b406e9195ce2130169af4579c8b0a2ff99db4616e798c"},"schema_version":"1.0"},"canonical_sha256":"678ee819b14cb7a11fbd17a14bce87136cb98ead8bec320b3f3678b0a80b62bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:37.034663Z","signature_b64":"PNg5BTiIqes7YHBTQ1HkCm5TV7ADs2NF5RNdYmalxbCWZyTvXjUAOO9JwE0cCnGuDZkD45UoAZBt+/FJn3WzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"678ee819b14cb7a11fbd17a14bce87136cb98ead8bec320b3f3678b0a80b62bc","last_reissued_at":"2026-05-18T00:47:37.034172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:37.034172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07654","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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SmpdfXp+qXywwC1UsRJU0jJ6rCvpLVCuO1qodNTJRj1SJVwwu3j1DRA/g4fvn79eb/4RuECwRxg17W68yPLOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:13:06.094833Z"},"content_sha256":"e37d2f9254123a5e416044c3c317b6af7cd22ad9b795c9bc31f0ece11e5c690a","schema_version":"1.0","event_id":"sha256:e37d2f9254123a5e416044c3c317b6af7cd22ad9b795c9bc31f0ece11e5c690a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:M6HOQGNRJS32CH55C6QUXTUHCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Users' Guide to Infra-nilmanifolds and Almost-Bieberbach groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Karel Dekimpe","submitted_at":"2016-03-24T16:48:10Z","abstract_excerpt":"The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the results, we refer to the literature. Nevertheless, at certain places we offer a somewhat different and new approach and in these cases we provide full proofs. We have tried to keep the prerequisites as minimal as possible. We also provide completely worked out examples, with explicit computations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07654","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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h+c6zDExVx+PUIuRVjBQHgSucVvG+g+29jz1fTi00NWvxDtyE3wUm+vjjM8thDwuTE7LimzGRyMMerWBxlMDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:13:06.095161Z"},"content_sha256":"06b73c02d7837a346ae1f86c58819c078f7134d54d1c55d78c3f376509ab22cd","schema_version":"1.0","event_id":"sha256:06b73c02d7837a346ae1f86c58819c078f7134d54d1c55d78c3f376509ab22cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6HOQGNRJS32CH55C6QUXTUHCN/bundle.json","state_url":"https://pith.science/pith/M6HOQGNRJS32CH55C6QUXTUHCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6HOQGNRJS32CH55C6QUXTUHCN/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":"2026-06-29T14:13:06Z","links":{"resolver":"https://pith.science/pith/M6HOQGNRJS32CH55C6QUXTUHCN","bundle":"https://pith.science/pith/M6HOQGNRJS32CH55C6QUXTUHCN/bundle.json","state":"https://pith.science/pith/M6HOQGNRJS32CH55C6QUXTUHCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6HOQGNRJS32CH55C6QUXTUHCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M6HOQGNRJS32CH55C6QUXTUHCN","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":"c447cdce036cf058857b406e9195ce2130169af4579c8b0a2ff99db4616e798c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-24T16:48:10Z","title_canon_sha256":"fd40bda3a2a810eaa7027452ec98049befb94c7f931d8c1fb374539b47551417"},"schema_version":"1.0","source":{"id":"1603.07654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07654","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07654v2","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07654","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"M6HOQGNRJS32","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6HOQGNRJS32CH55","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6HOQGNR","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:06b73c02d7837a346ae1f86c58819c078f7134d54d1c55d78c3f376509ab22cd","target":"graph","created_at":"2026-05-18T00:47:37Z","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":"The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the results, we refer to the literature. Nevertheless, at certain places we offer a somewhat different and new approach and in these cases we provide full proofs. We have tried to keep the prerequisites as minimal as possible. We also provide completely worked out examples, with explicit computations.","authors_text":"Karel Dekimpe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-24T16:48:10Z","title":"A Users' Guide to Infra-nilmanifolds and Almost-Bieberbach groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07654","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:e37d2f9254123a5e416044c3c317b6af7cd22ad9b795c9bc31f0ece11e5c690a","target":"record","created_at":"2026-05-18T00:47:37Z","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":"c447cdce036cf058857b406e9195ce2130169af4579c8b0a2ff99db4616e798c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-24T16:48:10Z","title_canon_sha256":"fd40bda3a2a810eaa7027452ec98049befb94c7f931d8c1fb374539b47551417"},"schema_version":"1.0","source":{"id":"1603.07654","kind":"arxiv","version":2}},"canonical_sha256":"678ee819b14cb7a11fbd17a14bce87136cb98ead8bec320b3f3678b0a80b62bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"678ee819b14cb7a11fbd17a14bce87136cb98ead8bec320b3f3678b0a80b62bc","first_computed_at":"2026-05-18T00:47:37.034172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:37.034172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PNg5BTiIqes7YHBTQ1HkCm5TV7ADs2NF5RNdYmalxbCWZyTvXjUAOO9JwE0cCnGuDZkD45UoAZBt+/FJn3WzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:37.034663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e37d2f9254123a5e416044c3c317b6af7cd22ad9b795c9bc31f0ece11e5c690a","sha256:06b73c02d7837a346ae1f86c58819c078f7134d54d1c55d78c3f376509ab22cd"],"state_sha256":"233e68ce7e0ef1152eb134d80580c2ac827fc475c9f28f1e1d60b2f4d980bade"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ynsmlh9Td7tFewgFgYw520/QPtlaUP0yL8iedml0R7PVIlVhNcc4kCS98jge/OB6LpK+Hixnn24AE/gCxrOrBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:13:06.097004Z","bundle_sha256":"87edf2856dd5de1d5984efc12d7be8202da13451ddd25b28fd0be2bc759e0fa5"}}