{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KU3VWQ2XKTM4ZGQB43LUBZVNM6","short_pith_number":"pith:KU3VWQ2X","canonical_record":{"source":{"id":"1705.08768","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:56:32Z","cross_cats_sorted":[],"title_canon_sha256":"cee9c3895caee99b3a9e06efadcd3d044985281629cbaa3153381f87b0b60662","abstract_canon_sha256":"d90557c2a62274a8edadd3bca65524aacc06fa0c5561c9463d416f2d3bf4e5c6"},"schema_version":"1.0"},"canonical_sha256":"55375b435754d9cc9a01e6d740e6ad679cf566b856da1e896b2af8de7b45b8bf","source":{"kind":"arxiv","id":"1705.08768","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08768","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08768v1","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08768","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"KU3VWQ2XKTM4","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KU3VWQ2XKTM4ZGQB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KU3VWQ2X","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KU3VWQ2XKTM4ZGQB43LUBZVNM6","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08768","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:56:32Z","cross_cats_sorted":[],"title_canon_sha256":"cee9c3895caee99b3a9e06efadcd3d044985281629cbaa3153381f87b0b60662","abstract_canon_sha256":"d90557c2a62274a8edadd3bca65524aacc06fa0c5561c9463d416f2d3bf4e5c6"},"schema_version":"1.0"},"canonical_sha256":"55375b435754d9cc9a01e6d740e6ad679cf566b856da1e896b2af8de7b45b8bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:44.314201Z","signature_b64":"jc7t7oslILm+/KK/Z8Y0A70AdATe09LOWUSDkyw7690C1fsKKc4ak6+8QdSUMn4HBHVb4oZMm6iGSHFZ6FzjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55375b435754d9cc9a01e6d740e6ad679cf566b856da1e896b2af8de7b45b8bf","last_reissued_at":"2026-05-18T00:43:44.313782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:44.313782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08768","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":"2026-05-18T00:43:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sjj/o6zWlon2dVguECNufk1II4bAOjHYABf1ljJpNws6o9XunJEcrmhwOSaYNsaITRo9nfn3OETjYJ439x+9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:15:49.381817Z"},"content_sha256":"bfed153c38d68b373b92a6eb68e779e1bfe28d9376e0b92ffc9660b3fe00b8fb","schema_version":"1.0","event_id":"sha256:bfed153c38d68b373b92a6eb68e779e1bfe28d9376e0b92ffc9660b3fe00b8fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KU3VWQ2XKTM4ZGQB43LUBZVNM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Threshold functions for small subgraphs: an analytic approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernhard Gittenberger, Dani\\`ele Gardy, \\'Elie de Panafieu, Gwendal Collet, Vlady Ravelomanana","submitted_at":"2017-05-24T13:56:32Z","abstract_excerpt":"We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to describe the possible overlapping of copies.\n  This paper is a version, extended to include proofs, of the paper with the same title to be presented at the Eurocomb 2017 meeting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08768","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":"2026-05-18T00:43:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PZx/ad9IT5hoSKd5Z00LN0qDuLc/uCBEJA5GNYxBco4lXSpD2UmiSbTV6im8NYyLNaLkfhN5R9m08TYq/ahmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:15:49.382415Z"},"content_sha256":"94cdbeecceabec49d9eeb3cdab96a1c8c945e17e8f98ff95d94a5592ee0dddb3","schema_version":"1.0","event_id":"sha256:94cdbeecceabec49d9eeb3cdab96a1c8c945e17e8f98ff95d94a5592ee0dddb3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KU3VWQ2XKTM4ZGQB43LUBZVNM6/bundle.json","state_url":"https://pith.science/pith/KU3VWQ2XKTM4ZGQB43LUBZVNM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KU3VWQ2XKTM4ZGQB43LUBZVNM6/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":"2026-05-27T07:15:49Z","links":{"resolver":"https://pith.science/pith/KU3VWQ2XKTM4ZGQB43LUBZVNM6","bundle":"https://pith.science/pith/KU3VWQ2XKTM4ZGQB43LUBZVNM6/bundle.json","state":"https://pith.science/pith/KU3VWQ2XKTM4ZGQB43LUBZVNM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KU3VWQ2XKTM4ZGQB43LUBZVNM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KU3VWQ2XKTM4ZGQB43LUBZVNM6","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":"d90557c2a62274a8edadd3bca65524aacc06fa0c5561c9463d416f2d3bf4e5c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:56:32Z","title_canon_sha256":"cee9c3895caee99b3a9e06efadcd3d044985281629cbaa3153381f87b0b60662"},"schema_version":"1.0","source":{"id":"1705.08768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08768","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08768v1","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08768","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"KU3VWQ2XKTM4","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KU3VWQ2XKTM4ZGQB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KU3VWQ2X","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:94cdbeecceabec49d9eeb3cdab96a1c8c945e17e8f98ff95d94a5592ee0dddb3","target":"graph","created_at":"2026-05-18T00:43:44Z","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 revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to describe the possible overlapping of copies.\n  This paper is a version, extended to include proofs, of the paper with the same title to be presented at the Eurocomb 2017 meeting.","authors_text":"Bernhard Gittenberger, Dani\\`ele Gardy, \\'Elie de Panafieu, Gwendal Collet, Vlady Ravelomanana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:56:32Z","title":"Threshold functions for small subgraphs: an analytic approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08768","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:bfed153c38d68b373b92a6eb68e779e1bfe28d9376e0b92ffc9660b3fe00b8fb","target":"record","created_at":"2026-05-18T00:43:44Z","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":"d90557c2a62274a8edadd3bca65524aacc06fa0c5561c9463d416f2d3bf4e5c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:56:32Z","title_canon_sha256":"cee9c3895caee99b3a9e06efadcd3d044985281629cbaa3153381f87b0b60662"},"schema_version":"1.0","source":{"id":"1705.08768","kind":"arxiv","version":1}},"canonical_sha256":"55375b435754d9cc9a01e6d740e6ad679cf566b856da1e896b2af8de7b45b8bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55375b435754d9cc9a01e6d740e6ad679cf566b856da1e896b2af8de7b45b8bf","first_computed_at":"2026-05-18T00:43:44.313782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:44.313782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jc7t7oslILm+/KK/Z8Y0A70AdATe09LOWUSDkyw7690C1fsKKc4ak6+8QdSUMn4HBHVb4oZMm6iGSHFZ6FzjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:44.314201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfed153c38d68b373b92a6eb68e779e1bfe28d9376e0b92ffc9660b3fe00b8fb","sha256:94cdbeecceabec49d9eeb3cdab96a1c8c945e17e8f98ff95d94a5592ee0dddb3"],"state_sha256":"ca06c4d8b68c1c347d10fc59381860b686b24234266f6a79f299b05ce6753fb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0GkmFEfP9bf06be2gtEneiMMeQDwDQsMchqY65l5GGoxpl91dMmZ7iFWnRuF6kRoF2lXC8RvRvNSTJyGMdrvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:15:49.385877Z","bundle_sha256":"e9f548dbfbcd8503a7881538f17f7bb6d0dd8995a05548197c90ab90ffdb5192"}}