{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:QDTCGAB4CQ5LUTHMKS7N7TTPUV","short_pith_number":"pith:QDTCGAB4","canonical_record":{"source":{"id":"0710.4982","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-10-26T03:22:57Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"be49240fae674115a3abc7515dfcd2231228c6d7f33ea10eea418cd86063f107","abstract_canon_sha256":"61b6c052f3fa1efb9ec15ba6958a74df08337c5231c6a522e6c0f012507509bb"},"schema_version":"1.0"},"canonical_sha256":"80e623003c143aba4cec54bedfce6fa554ff96610376297c1fcb1073a02bc5d2","source":{"kind":"arxiv","id":"0710.4982","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.4982","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"arxiv_version","alias_value":"0710.4982v1","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.4982","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"pith_short_12","alias_value":"QDTCGAB4CQ5L","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"QDTCGAB4CQ5LUTHM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"QDTCGAB4","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:QDTCGAB4CQ5LUTHMKS7N7TTPUV","target":"record","payload":{"canonical_record":{"source":{"id":"0710.4982","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-10-26T03:22:57Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"be49240fae674115a3abc7515dfcd2231228c6d7f33ea10eea418cd86063f107","abstract_canon_sha256":"61b6c052f3fa1efb9ec15ba6958a74df08337c5231c6a522e6c0f012507509bb"},"schema_version":"1.0"},"canonical_sha256":"80e623003c143aba4cec54bedfce6fa554ff96610376297c1fcb1073a02bc5d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:06.111000Z","signature_b64":"dLCl87oeOQB9Me9iOT2EvOfaAHCOmtnis/TeSrZoJIrKYKZ1B/iJgGyldJ3q8RJqgyRiyhq6Df9dtJ3FyHFlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80e623003c143aba4cec54bedfce6fa554ff96610376297c1fcb1073a02bc5d2","last_reissued_at":"2026-05-18T04:14:06.110510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:06.110510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.4982","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":"2026-05-18T04:14:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoVxFH7BO7idJxtZdT1bs6g+DwHVj85rCGFH7VTtZ0GN4o0zWrRrrT5RbLfDFf+g/97u54GGT8Y2T55IoeGlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:34:52.114645Z"},"content_sha256":"a56fe608b6004cbb515310f2a4b6819f36278b262f05f58a5afec1865c6ff2f8","schema_version":"1.0","event_id":"sha256:a56fe608b6004cbb515310f2a4b6819f36278b262f05f58a5afec1865c6ff2f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:QDTCGAB4CQ5LUTHMKS7N7TTPUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First to Market is not Everything: an Analysis of Preferential Attachment with Fitness","license":"","headline":"","cross_cats":["cs.SI"],"primary_cat":"math.PR","authors_text":"Christian Borgs, Constantinos Daskalakis, Jennifer Chayes, Sebastien Roch","submitted_at":"2007-10-26T03:22:57Z","abstract_excerpt":"In this paper, we provide a rigorous analysis of preferential attachment with fitness, a random graph model introduced by Bianconi and Barabasi. Depending on the shape of the fitness distribution, we observe three distinct phases: a first-mover-advantage phase, a fit-get-richer phase and an innovation-pays-off phase."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4982","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":"2026-05-18T04:14:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1t6BG92W6Lygm2JlS/r7lpFTETjLpqE9a+9tNYzCPfU7XNhNdy31506/PGDVuuA1mjMB02RXYi0erU0YupxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:34:52.114997Z"},"content_sha256":"0ac081c024aa106bb07e1dcf4fee4d57b9117bcd6f0258a00e26994178e9d1c5","schema_version":"1.0","event_id":"sha256:0ac081c024aa106bb07e1dcf4fee4d57b9117bcd6f0258a00e26994178e9d1c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDTCGAB4CQ5LUTHMKS7N7TTPUV/bundle.json","state_url":"https://pith.science/pith/QDTCGAB4CQ5LUTHMKS7N7TTPUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDTCGAB4CQ5LUTHMKS7N7TTPUV/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":"2026-05-29T18:34:52Z","links":{"resolver":"https://pith.science/pith/QDTCGAB4CQ5LUTHMKS7N7TTPUV","bundle":"https://pith.science/pith/QDTCGAB4CQ5LUTHMKS7N7TTPUV/bundle.json","state":"https://pith.science/pith/QDTCGAB4CQ5LUTHMKS7N7TTPUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDTCGAB4CQ5LUTHMKS7N7TTPUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:QDTCGAB4CQ5LUTHMKS7N7TTPUV","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":"61b6c052f3fa1efb9ec15ba6958a74df08337c5231c6a522e6c0f012507509bb","cross_cats_sorted":["cs.SI"],"license":"","primary_cat":"math.PR","submitted_at":"2007-10-26T03:22:57Z","title_canon_sha256":"be49240fae674115a3abc7515dfcd2231228c6d7f33ea10eea418cd86063f107"},"schema_version":"1.0","source":{"id":"0710.4982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.4982","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"arxiv_version","alias_value":"0710.4982v1","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.4982","created_at":"2026-05-18T04:14:06Z"},{"alias_kind":"pith_short_12","alias_value":"QDTCGAB4CQ5L","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"QDTCGAB4CQ5LUTHM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"QDTCGAB4","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:0ac081c024aa106bb07e1dcf4fee4d57b9117bcd6f0258a00e26994178e9d1c5","target":"graph","created_at":"2026-05-18T04:14:06Z","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":"In this paper, we provide a rigorous analysis of preferential attachment with fitness, a random graph model introduced by Bianconi and Barabasi. Depending on the shape of the fitness distribution, we observe three distinct phases: a first-mover-advantage phase, a fit-get-richer phase and an innovation-pays-off phase.","authors_text":"Christian Borgs, Constantinos Daskalakis, Jennifer Chayes, Sebastien Roch","cross_cats":["cs.SI"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-10-26T03:22:57Z","title":"First to Market is not Everything: an Analysis of Preferential Attachment with Fitness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4982","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:a56fe608b6004cbb515310f2a4b6819f36278b262f05f58a5afec1865c6ff2f8","target":"record","created_at":"2026-05-18T04:14:06Z","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":"61b6c052f3fa1efb9ec15ba6958a74df08337c5231c6a522e6c0f012507509bb","cross_cats_sorted":["cs.SI"],"license":"","primary_cat":"math.PR","submitted_at":"2007-10-26T03:22:57Z","title_canon_sha256":"be49240fae674115a3abc7515dfcd2231228c6d7f33ea10eea418cd86063f107"},"schema_version":"1.0","source":{"id":"0710.4982","kind":"arxiv","version":1}},"canonical_sha256":"80e623003c143aba4cec54bedfce6fa554ff96610376297c1fcb1073a02bc5d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80e623003c143aba4cec54bedfce6fa554ff96610376297c1fcb1073a02bc5d2","first_computed_at":"2026-05-18T04:14:06.110510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:06.110510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLCl87oeOQB9Me9iOT2EvOfaAHCOmtnis/TeSrZoJIrKYKZ1B/iJgGyldJ3q8RJqgyRiyhq6Df9dtJ3FyHFlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:06.111000Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.4982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a56fe608b6004cbb515310f2a4b6819f36278b262f05f58a5afec1865c6ff2f8","sha256:0ac081c024aa106bb07e1dcf4fee4d57b9117bcd6f0258a00e26994178e9d1c5"],"state_sha256":"2ad39537f7b2ae94a0ef50a2f4aa6ca712f3c75ce0a5e1fc919479ae53d57220"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YdPJ13NNXKGEIfy4x7rNEV9enftyrYyX6Fql6WGCSat1MWTU8oi3mtFclHhYnibmP8qSx9eGckhiKlsTJ5xZDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:34:52.116950Z","bundle_sha256":"48f454910ac93eadd2240d8d872fcc5710f5a411b91540761b3bb9b57b7e5a7b"}}